Properties

Label 9600.2.a
Level $9600$
Weight $2$
Character orbit 9600.a
Rep. character $\chi_{9600}(1,\cdot)$
Character field $\Q$
Dimension $152$
Newform subspaces $100$
Sturm bound $3840$
Trace bound $17$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 9600 = 2^{7} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9600.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 100 \)
Sturm bound: \(3840\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\), \(17\), \(29\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9600))\).

Total New Old
Modular forms 2016 152 1864
Cusp forms 1825 152 1673
Eisenstein series 191 0 191

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(3\)\(5\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(17\)
\(+\)\(+\)\(-\)\(-\)\(22\)
\(+\)\(-\)\(+\)\(-\)\(19\)
\(+\)\(-\)\(-\)\(+\)\(18\)
\(-\)\(+\)\(+\)\(-\)\(19\)
\(-\)\(+\)\(-\)\(+\)\(18\)
\(-\)\(-\)\(+\)\(+\)\(17\)
\(-\)\(-\)\(-\)\(-\)\(22\)
Plus space\(+\)\(70\)
Minus space\(-\)\(82\)

Trace form

\( 152q + 152q^{9} + O(q^{10}) \) \( 152q + 152q^{9} - 16q^{17} - 16q^{41} + 120q^{49} - 32q^{57} + 16q^{73} + 152q^{81} + 48q^{89} - 80q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9600))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 5
9600.2.a.a \(1\) \(76.656\) \(\Q\) None \(0\) \(-1\) \(0\) \(-4\) \(+\) \(+\) \(+\) \(q-q^{3}-4q^{7}+q^{9}-6q^{11}+4q^{13}+\cdots\)
9600.2.a.b \(1\) \(76.656\) \(\Q\) None \(0\) \(-1\) \(0\) \(-4\) \(-\) \(+\) \(+\) \(q-q^{3}-4q^{7}+q^{9}-2q^{11}+4q^{21}+\cdots\)
9600.2.a.c \(1\) \(76.656\) \(\Q\) None \(0\) \(-1\) \(0\) \(-4\) \(+\) \(+\) \(-\) \(q-q^{3}-4q^{7}+q^{9}-6q^{13}-2q^{17}+\cdots\)
9600.2.a.d \(1\) \(76.656\) \(\Q\) None \(0\) \(-1\) \(0\) \(-4\) \(+\) \(+\) \(-\) \(q-q^{3}-4q^{7}+q^{9}+6q^{13}+2q^{17}+\cdots\)
9600.2.a.e \(1\) \(76.656\) \(\Q\) None \(0\) \(-1\) \(0\) \(-2\) \(-\) \(+\) \(+\) \(q-q^{3}-2q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
9600.2.a.f \(1\) \(76.656\) \(\Q\) None \(0\) \(-1\) \(0\) \(-2\) \(-\) \(+\) \(+\) \(q-q^{3}-2q^{7}+q^{9}-2q^{11}-6q^{13}+\cdots\)
9600.2.a.g \(1\) \(76.656\) \(\Q\) None \(0\) \(-1\) \(0\) \(-2\) \(+\) \(+\) \(+\) \(q-q^{3}-2q^{7}+q^{9}+2q^{11}-2q^{13}+\cdots\)
9600.2.a.h \(1\) \(76.656\) \(\Q\) None \(0\) \(-1\) \(0\) \(-2\) \(-\) \(+\) \(+\) \(q-q^{3}-2q^{7}+q^{9}+4q^{11}+6q^{13}+\cdots\)
9600.2.a.i \(1\) \(76.656\) \(\Q\) None \(0\) \(-1\) \(0\) \(-2\) \(-\) \(+\) \(+\) \(q-q^{3}-2q^{7}+q^{9}+6q^{11}+2q^{13}+\cdots\)
9600.2.a.j \(1\) \(76.656\) \(\Q\) None \(0\) \(-1\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q-q^{3}+q^{9}-4q^{11}-2q^{13}+2q^{17}+\cdots\)
9600.2.a.k \(1\) \(76.656\) \(\Q\) None \(0\) \(-1\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q-q^{3}+q^{9}-4q^{11}+2q^{13}+2q^{17}+\cdots\)
9600.2.a.l \(1\) \(76.656\) \(\Q\) None \(0\) \(-1\) \(0\) \(0\) \(+\) \(+\) \(+\) \(q-q^{3}+q^{9}-2q^{11}-4q^{13}-q^{27}+\cdots\)
9600.2.a.m \(1\) \(76.656\) \(\Q\) None \(0\) \(-1\) \(0\) \(0\) \(+\) \(+\) \(-\) \(q-q^{3}+q^{9}-2q^{11}-2q^{13}-2q^{17}+\cdots\)
9600.2.a.n \(1\) \(76.656\) \(\Q\) None \(0\) \(-1\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q-q^{3}+q^{9}-2q^{11}+2q^{13}-2q^{17}+\cdots\)
9600.2.a.o \(1\) \(76.656\) \(\Q\) None \(0\) \(-1\) \(0\) \(0\) \(+\) \(+\) \(+\) \(q-q^{3}+q^{9}-2q^{11}+4q^{13}-q^{27}+\cdots\)
9600.2.a.p \(1\) \(76.656\) \(\Q\) None \(0\) \(-1\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q-q^{3}+q^{9}+2q^{11}-2q^{13}+2q^{17}+\cdots\)
9600.2.a.q \(1\) \(76.656\) \(\Q\) None \(0\) \(-1\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q-q^{3}+q^{9}+2q^{11}+2q^{13}+2q^{17}+\cdots\)
9600.2.a.r \(1\) \(76.656\) \(\Q\) None \(0\) \(-1\) \(0\) \(0\) \(+\) \(+\) \(-\) \(q-q^{3}+q^{9}+4q^{11}-2q^{13}-2q^{17}+\cdots\)
9600.2.a.s \(1\) \(76.656\) \(\Q\) None \(0\) \(-1\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q-q^{3}+q^{9}+4q^{11}+2q^{13}-2q^{17}+\cdots\)
9600.2.a.t \(1\) \(76.656\) \(\Q\) None \(0\) \(-1\) \(0\) \(2\) \(+\) \(+\) \(+\) \(q-q^{3}+2q^{7}+q^{9}-4q^{11}-2q^{13}+\cdots\)
9600.2.a.u \(1\) \(76.656\) \(\Q\) None \(0\) \(-1\) \(0\) \(2\) \(-\) \(+\) \(+\) \(q-q^{3}+2q^{7}+q^{9}-2q^{11}+6q^{13}+\cdots\)
9600.2.a.v \(1\) \(76.656\) \(\Q\) None \(0\) \(-1\) \(0\) \(2\) \(+\) \(+\) \(+\) \(q-q^{3}+2q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots\)
9600.2.a.w \(1\) \(76.656\) \(\Q\) None \(0\) \(-1\) \(0\) \(2\) \(-\) \(+\) \(+\) \(q-q^{3}+2q^{7}+q^{9}+4q^{11}-6q^{13}+\cdots\)
9600.2.a.x \(1\) \(76.656\) \(\Q\) None \(0\) \(-1\) \(0\) \(2\) \(+\) \(+\) \(+\) \(q-q^{3}+2q^{7}+q^{9}+6q^{11}-2q^{13}+\cdots\)
9600.2.a.y \(1\) \(76.656\) \(\Q\) None \(0\) \(-1\) \(0\) \(4\) \(-\) \(+\) \(+\) \(q-q^{3}+4q^{7}+q^{9}-6q^{11}-4q^{13}+\cdots\)
9600.2.a.z \(1\) \(76.656\) \(\Q\) None \(0\) \(-1\) \(0\) \(4\) \(-\) \(+\) \(+\) \(q-q^{3}+4q^{7}+q^{9}-2q^{11}-4q^{21}+\cdots\)
9600.2.a.ba \(1\) \(76.656\) \(\Q\) None \(0\) \(-1\) \(0\) \(4\) \(-\) \(+\) \(-\) \(q-q^{3}+4q^{7}+q^{9}-6q^{13}+2q^{17}+\cdots\)
9600.2.a.bb \(1\) \(76.656\) \(\Q\) None \(0\) \(-1\) \(0\) \(4\) \(+\) \(+\) \(-\) \(q-q^{3}+4q^{7}+q^{9}+6q^{13}-2q^{17}+\cdots\)
9600.2.a.bc \(1\) \(76.656\) \(\Q\) None \(0\) \(1\) \(0\) \(-4\) \(-\) \(-\) \(-\) \(q+q^{3}-4q^{7}+q^{9}-6q^{13}+2q^{17}+\cdots\)
9600.2.a.bd \(1\) \(76.656\) \(\Q\) None \(0\) \(1\) \(0\) \(-4\) \(+\) \(-\) \(-\) \(q+q^{3}-4q^{7}+q^{9}+6q^{13}-2q^{17}+\cdots\)
9600.2.a.be \(1\) \(76.656\) \(\Q\) None \(0\) \(1\) \(0\) \(-4\) \(-\) \(-\) \(+\) \(q+q^{3}-4q^{7}+q^{9}+2q^{11}-4q^{21}+\cdots\)
9600.2.a.bf \(1\) \(76.656\) \(\Q\) None \(0\) \(1\) \(0\) \(-4\) \(+\) \(-\) \(+\) \(q+q^{3}-4q^{7}+q^{9}+6q^{11}-4q^{13}+\cdots\)
9600.2.a.bg \(1\) \(76.656\) \(\Q\) None \(0\) \(1\) \(0\) \(-2\) \(+\) \(-\) \(+\) \(q+q^{3}-2q^{7}+q^{9}-6q^{11}-2q^{13}+\cdots\)
9600.2.a.bh \(1\) \(76.656\) \(\Q\) None \(0\) \(1\) \(0\) \(-2\) \(+\) \(-\) \(+\) \(q+q^{3}-2q^{7}+q^{9}-4q^{11}-6q^{13}+\cdots\)
9600.2.a.bi \(1\) \(76.656\) \(\Q\) None \(0\) \(1\) \(0\) \(-2\) \(-\) \(-\) \(+\) \(q+q^{3}-2q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots\)
9600.2.a.bj \(1\) \(76.656\) \(\Q\) None \(0\) \(1\) \(0\) \(-2\) \(+\) \(-\) \(+\) \(q+q^{3}-2q^{7}+q^{9}+2q^{11}+6q^{13}+\cdots\)
9600.2.a.bk \(1\) \(76.656\) \(\Q\) None \(0\) \(1\) \(0\) \(-2\) \(+\) \(-\) \(+\) \(q+q^{3}-2q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots\)
9600.2.a.bl \(1\) \(76.656\) \(\Q\) None \(0\) \(1\) \(0\) \(0\) \(+\) \(-\) \(-\) \(q+q^{3}+q^{9}-4q^{11}-2q^{13}-2q^{17}+\cdots\)
9600.2.a.bm \(1\) \(76.656\) \(\Q\) None \(0\) \(1\) \(0\) \(0\) \(+\) \(-\) \(-\) \(q+q^{3}+q^{9}-4q^{11}+2q^{13}-2q^{17}+\cdots\)
9600.2.a.bn \(1\) \(76.656\) \(\Q\) None \(0\) \(1\) \(0\) \(0\) \(+\) \(-\) \(-\) \(q+q^{3}+q^{9}-2q^{11}-2q^{13}+2q^{17}+\cdots\)
9600.2.a.bo \(1\) \(76.656\) \(\Q\) None \(0\) \(1\) \(0\) \(0\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{9}-2q^{11}+2q^{13}+2q^{17}+\cdots\)
9600.2.a.bp \(1\) \(76.656\) \(\Q\) None \(0\) \(1\) \(0\) \(0\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{9}+2q^{11}-4q^{13}+q^{27}+\cdots\)
9600.2.a.bq \(1\) \(76.656\) \(\Q\) None \(0\) \(1\) \(0\) \(0\) \(+\) \(-\) \(-\) \(q+q^{3}+q^{9}+2q^{11}-2q^{13}-2q^{17}+\cdots\)
9600.2.a.br \(1\) \(76.656\) \(\Q\) None \(0\) \(1\) \(0\) \(0\) \(+\) \(-\) \(-\) \(q+q^{3}+q^{9}+2q^{11}+2q^{13}-2q^{17}+\cdots\)
9600.2.a.bs \(1\) \(76.656\) \(\Q\) None \(0\) \(1\) \(0\) \(0\) \(+\) \(-\) \(+\) \(q+q^{3}+q^{9}+2q^{11}+4q^{13}+q^{27}+\cdots\)
9600.2.a.bt \(1\) \(76.656\) \(\Q\) None \(0\) \(1\) \(0\) \(0\) \(+\) \(-\) \(-\) \(q+q^{3}+q^{9}+4q^{11}-2q^{13}+2q^{17}+\cdots\)
9600.2.a.bu \(1\) \(76.656\) \(\Q\) None \(0\) \(1\) \(0\) \(0\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{9}+4q^{11}+2q^{13}+2q^{17}+\cdots\)
9600.2.a.bv \(1\) \(76.656\) \(\Q\) None \(0\) \(1\) \(0\) \(2\) \(+\) \(-\) \(+\) \(q+q^{3}+2q^{7}+q^{9}-6q^{11}+2q^{13}+\cdots\)
9600.2.a.bw \(1\) \(76.656\) \(\Q\) None \(0\) \(1\) \(0\) \(2\) \(-\) \(-\) \(+\) \(q+q^{3}+2q^{7}+q^{9}-4q^{11}+6q^{13}+\cdots\)
9600.2.a.bx \(1\) \(76.656\) \(\Q\) None \(0\) \(1\) \(0\) \(2\) \(+\) \(-\) \(+\) \(q+q^{3}+2q^{7}+q^{9}-2q^{11}-2q^{13}+\cdots\)
9600.2.a.by \(1\) \(76.656\) \(\Q\) None \(0\) \(1\) \(0\) \(2\) \(-\) \(-\) \(+\) \(q+q^{3}+2q^{7}+q^{9}+2q^{11}-6q^{13}+\cdots\)
9600.2.a.bz \(1\) \(76.656\) \(\Q\) None \(0\) \(1\) \(0\) \(2\) \(+\) \(-\) \(+\) \(q+q^{3}+2q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
9600.2.a.ca \(1\) \(76.656\) \(\Q\) None \(0\) \(1\) \(0\) \(4\) \(-\) \(-\) \(-\) \(q+q^{3}+4q^{7}+q^{9}-6q^{13}-2q^{17}+\cdots\)
9600.2.a.cb \(1\) \(76.656\) \(\Q\) None \(0\) \(1\) \(0\) \(4\) \(-\) \(-\) \(-\) \(q+q^{3}+4q^{7}+q^{9}+6q^{13}+2q^{17}+\cdots\)
9600.2.a.cc \(1\) \(76.656\) \(\Q\) None \(0\) \(1\) \(0\) \(4\) \(+\) \(-\) \(+\) \(q+q^{3}+4q^{7}+q^{9}+2q^{11}+4q^{21}+\cdots\)
9600.2.a.cd \(1\) \(76.656\) \(\Q\) None \(0\) \(1\) \(0\) \(4\) \(+\) \(-\) \(+\) \(q+q^{3}+4q^{7}+q^{9}+6q^{11}+4q^{13}+\cdots\)
9600.2.a.ce \(2\) \(76.656\) \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(0\) \(-2\) \(+\) \(+\) \(-\) \(q-q^{3}+(-1+\beta )q^{7}+q^{9}+(-2+3\beta )q^{11}+\cdots\)
9600.2.a.cf \(2\) \(76.656\) \(\Q(\sqrt{6}) \) None \(0\) \(-2\) \(0\) \(-2\) \(-\) \(+\) \(+\) \(q-q^{3}+(-1+\beta )q^{7}+q^{9}+(-2-\beta )q^{11}+\cdots\)
9600.2.a.cg \(2\) \(76.656\) \(\Q(\sqrt{6}) \) None \(0\) \(-2\) \(0\) \(-2\) \(-\) \(+\) \(-\) \(q-q^{3}+(-1+\beta )q^{7}+q^{9}+\beta q^{11}+\cdots\)
9600.2.a.ch \(2\) \(76.656\) \(\Q(\sqrt{10}) \) None \(0\) \(-2\) \(0\) \(-2\) \(-\) \(+\) \(-\) \(q-q^{3}+(-1+\beta )q^{7}+q^{9}-\beta q^{11}+\cdots\)
9600.2.a.ci \(2\) \(76.656\) \(\Q(\sqrt{10}) \) None \(0\) \(-2\) \(0\) \(-2\) \(+\) \(+\) \(+\) \(q-q^{3}+(-1+\beta )q^{7}+q^{9}+\beta q^{11}+\cdots\)
9600.2.a.cj \(2\) \(76.656\) \(\Q(\sqrt{6}) \) None \(0\) \(-2\) \(0\) \(-2\) \(+\) \(+\) \(+\) \(q-q^{3}+(-1+\beta )q^{7}+q^{9}-\beta q^{11}+\cdots\)
9600.2.a.ck \(2\) \(76.656\) \(\Q(\sqrt{6}) \) None \(0\) \(-2\) \(0\) \(-2\) \(-\) \(+\) \(-\) \(q-q^{3}+(-1+\beta )q^{7}+q^{9}+(2+\beta )q^{11}+\cdots\)
9600.2.a.cl \(2\) \(76.656\) \(\Q(\sqrt{17}) \) None \(0\) \(-2\) \(0\) \(-2\) \(+\) \(+\) \(+\) \(q-q^{3}+(-1-\beta )q^{7}+q^{9}+2q^{11}+\cdots\)
9600.2.a.cm \(2\) \(76.656\) \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(0\) \(-2\) \(+\) \(+\) \(+\) \(q-q^{3}+(-1+\beta )q^{7}+q^{9}+(2-3\beta )q^{11}+\cdots\)
9600.2.a.cn \(2\) \(76.656\) \(\Q(\sqrt{6}) \) None \(0\) \(-2\) \(0\) \(2\) \(-\) \(+\) \(+\) \(q-q^{3}+(1+\beta )q^{7}+q^{9}+(-2+\beta )q^{11}+\cdots\)
9600.2.a.co \(2\) \(76.656\) \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(0\) \(2\) \(+\) \(+\) \(-\) \(q-q^{3}+(1+\beta )q^{7}+q^{9}+(-2-3\beta )q^{11}+\cdots\)
9600.2.a.cp \(2\) \(76.656\) \(\Q(\sqrt{10}) \) None \(0\) \(-2\) \(0\) \(2\) \(+\) \(+\) \(+\) \(q-q^{3}+(1+\beta )q^{7}+q^{9}-\beta q^{11}-q^{13}+\cdots\)
9600.2.a.cq \(2\) \(76.656\) \(\Q(\sqrt{6}) \) None \(0\) \(-2\) \(0\) \(2\) \(-\) \(+\) \(+\) \(q-q^{3}+(1+\beta )q^{7}+q^{9}+\beta q^{11}+(-1+\cdots)q^{13}+\cdots\)
9600.2.a.cr \(2\) \(76.656\) \(\Q(\sqrt{6}) \) None \(0\) \(-2\) \(0\) \(2\) \(-\) \(+\) \(-\) \(q-q^{3}+(1+\beta )q^{7}+q^{9}-\beta q^{11}+(1+\cdots)q^{13}+\cdots\)
9600.2.a.cs \(2\) \(76.656\) \(\Q(\sqrt{10}) \) None \(0\) \(-2\) \(0\) \(2\) \(+\) \(+\) \(-\) \(q-q^{3}+(1+\beta )q^{7}+q^{9}+\beta q^{11}+q^{13}+\cdots\)
9600.2.a.ct \(2\) \(76.656\) \(\Q(\sqrt{17}) \) None \(0\) \(-2\) \(0\) \(2\) \(-\) \(+\) \(+\) \(q-q^{3}+(1+\beta )q^{7}+q^{9}+2q^{11}+(1+\cdots)q^{13}+\cdots\)
9600.2.a.cu \(2\) \(76.656\) \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(0\) \(2\) \(-\) \(+\) \(+\) \(q-q^{3}+(1+\beta )q^{7}+q^{9}+(2+3\beta )q^{11}+\cdots\)
9600.2.a.cv \(2\) \(76.656\) \(\Q(\sqrt{6}) \) None \(0\) \(-2\) \(0\) \(2\) \(+\) \(+\) \(-\) \(q-q^{3}+(1+\beta )q^{7}+q^{9}+(2-\beta )q^{11}+\cdots\)
9600.2.a.cw \(2\) \(76.656\) \(\Q(\sqrt{17}) \) None \(0\) \(2\) \(0\) \(-2\) \(-\) \(-\) \(+\) \(q+q^{3}+(-1-\beta )q^{7}+q^{9}-2q^{11}+\cdots\)
9600.2.a.cx \(2\) \(76.656\) \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(0\) \(-2\) \(-\) \(-\) \(+\) \(q+q^{3}+(-1+\beta )q^{7}+q^{9}+(-2+3\beta )q^{11}+\cdots\)
9600.2.a.cy \(2\) \(76.656\) \(\Q(\sqrt{6}) \) None \(0\) \(2\) \(0\) \(-2\) \(+\) \(-\) \(-\) \(q+q^{3}+(-1+\beta )q^{7}+q^{9}+(-2-\beta )q^{11}+\cdots\)
9600.2.a.cz \(2\) \(76.656\) \(\Q(\sqrt{10}) \) None \(0\) \(2\) \(0\) \(-2\) \(-\) \(-\) \(+\) \(q+q^{3}+(-1+\beta )q^{7}+q^{9}-\beta q^{11}+\cdots\)
9600.2.a.da \(2\) \(76.656\) \(\Q(\sqrt{6}) \) None \(0\) \(2\) \(0\) \(-2\) \(+\) \(-\) \(+\) \(q+q^{3}+(-1+\beta )q^{7}+q^{9}+\beta q^{11}+\cdots\)
9600.2.a.db \(2\) \(76.656\) \(\Q(\sqrt{6}) \) None \(0\) \(2\) \(0\) \(-2\) \(+\) \(-\) \(-\) \(q+q^{3}+(-1+\beta )q^{7}+q^{9}-\beta q^{11}+\cdots\)
9600.2.a.dc \(2\) \(76.656\) \(\Q(\sqrt{10}) \) None \(0\) \(2\) \(0\) \(-2\) \(-\) \(-\) \(-\) \(q+q^{3}+(-1+\beta )q^{7}+q^{9}+\beta q^{11}+\cdots\)
9600.2.a.dd \(2\) \(76.656\) \(\Q(\sqrt{6}) \) None \(0\) \(2\) \(0\) \(-2\) \(-\) \(-\) \(+\) \(q+q^{3}+(-1+\beta )q^{7}+q^{9}+(2+\beta )q^{11}+\cdots\)
9600.2.a.de \(2\) \(76.656\) \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(0\) \(-2\) \(+\) \(-\) \(-\) \(q+q^{3}+(-1+\beta )q^{7}+q^{9}+(2-3\beta )q^{11}+\cdots\)
9600.2.a.df \(2\) \(76.656\) \(\Q(\sqrt{6}) \) None \(0\) \(2\) \(0\) \(2\) \(+\) \(-\) \(-\) \(q+q^{3}+(1+\beta )q^{7}+q^{9}+(-2+\beta )q^{11}+\cdots\)
9600.2.a.dg \(2\) \(76.656\) \(\Q(\sqrt{17}) \) None \(0\) \(2\) \(0\) \(2\) \(-\) \(-\) \(+\) \(q+q^{3}+(1+\beta )q^{7}+q^{9}-2q^{11}+(-1+\cdots)q^{13}+\cdots\)
9600.2.a.dh \(2\) \(76.656\) \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(0\) \(2\) \(-\) \(-\) \(+\) \(q+q^{3}+(1+\beta )q^{7}+q^{9}+(-2-3\beta )q^{11}+\cdots\)
9600.2.a.di \(2\) \(76.656\) \(\Q(\sqrt{6}) \) None \(0\) \(2\) \(0\) \(2\) \(-\) \(-\) \(-\) \(q+q^{3}+(1+\beta )q^{7}+q^{9}+\beta q^{11}+(-1+\cdots)q^{13}+\cdots\)
9600.2.a.dj \(2\) \(76.656\) \(\Q(\sqrt{10}) \) None \(0\) \(2\) \(0\) \(2\) \(-\) \(-\) \(-\) \(q+q^{3}+(1+\beta )q^{7}+q^{9}-\beta q^{11}-q^{13}+\cdots\)
9600.2.a.dk \(2\) \(76.656\) \(\Q(\sqrt{10}) \) None \(0\) \(2\) \(0\) \(2\) \(+\) \(-\) \(+\) \(q+q^{3}+(1+\beta )q^{7}+q^{9}+\beta q^{11}+q^{13}+\cdots\)
9600.2.a.dl \(2\) \(76.656\) \(\Q(\sqrt{6}) \) None \(0\) \(2\) \(0\) \(2\) \(+\) \(-\) \(+\) \(q+q^{3}+(1+\beta )q^{7}+q^{9}-\beta q^{11}+(1+\cdots)q^{13}+\cdots\)
9600.2.a.dm \(2\) \(76.656\) \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(0\) \(2\) \(-\) \(-\) \(-\) \(q+q^{3}+(1+\beta )q^{7}+q^{9}+(2+3\beta )q^{11}+\cdots\)
9600.2.a.dn \(2\) \(76.656\) \(\Q(\sqrt{6}) \) None \(0\) \(2\) \(0\) \(2\) \(+\) \(-\) \(+\) \(q+q^{3}+(1+\beta )q^{7}+q^{9}+(2-\beta )q^{11}+\cdots\)
9600.2.a.do \(3\) \(76.656\) 3.3.148.1 None \(0\) \(-3\) \(0\) \(-4\) \(-\) \(+\) \(-\) \(q-q^{3}+(-1+\beta _{1})q^{7}+q^{9}+(-2-\beta _{2})q^{11}+\cdots\)
9600.2.a.dp \(3\) \(76.656\) 3.3.148.1 None \(0\) \(-3\) \(0\) \(-4\) \(+\) \(+\) \(-\) \(q-q^{3}+(-1+\beta _{1})q^{7}+q^{9}+(2+\beta _{2})q^{11}+\cdots\)
9600.2.a.dq \(3\) \(76.656\) 3.3.148.1 None \(0\) \(-3\) \(0\) \(4\) \(+\) \(+\) \(-\) \(q-q^{3}+(1-\beta _{1})q^{7}+q^{9}+(-2-\beta _{2})q^{11}+\cdots\)
9600.2.a.dr \(3\) \(76.656\) 3.3.148.1 None \(0\) \(-3\) \(0\) \(4\) \(+\) \(+\) \(-\) \(q-q^{3}+(1-\beta _{1})q^{7}+q^{9}+(2+\beta _{2})q^{11}+\cdots\)
9600.2.a.ds \(3\) \(76.656\) 3.3.148.1 None \(0\) \(3\) \(0\) \(-4\) \(-\) \(-\) \(-\) \(q+q^{3}+(-1+\beta _{1})q^{7}+q^{9}+(-2-\beta _{2})q^{11}+\cdots\)
9600.2.a.dt \(3\) \(76.656\) 3.3.148.1 None \(0\) \(3\) \(0\) \(-4\) \(-\) \(-\) \(-\) \(q+q^{3}+(-1+\beta _{1})q^{7}+q^{9}+(2+\beta _{2})q^{11}+\cdots\)
9600.2.a.du \(3\) \(76.656\) 3.3.148.1 None \(0\) \(3\) \(0\) \(4\) \(+\) \(-\) \(-\) \(q+q^{3}+(1-\beta _{1})q^{7}+q^{9}+(-2-\beta _{2})q^{11}+\cdots\)
9600.2.a.dv \(3\) \(76.656\) 3.3.148.1 None \(0\) \(3\) \(0\) \(4\) \(-\) \(-\) \(-\) \(q+q^{3}+(1-\beta _{1})q^{7}+q^{9}+(2+\beta _{2})q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9600))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(9600)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(100))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(128))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(150))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(160))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(192))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(200))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(240))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(300))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(320))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(384))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(400))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(480))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(600))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(640))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(800))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(960))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1200))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1600))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1920))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2400))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3200))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4800))\)\(^{\oplus 2}\)