Properties

Label 9792.2.a
Level $9792$
Weight $2$
Character orbit 9792.a
Rep. character $\chi_{9792}(1,\cdot)$
Character field $\Q$
Dimension $160$
Newform subspaces $96$
Sturm bound $3456$
Trace bound $29$

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Defining parameters

Level: \( N \) \(=\) \( 9792 = 2^{6} \cdot 3^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9792.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 96 \)
Sturm bound: \(3456\)
Trace bound: \(29\)
Distinguishing \(T_p\): \(5\), \(7\), \(11\), \(13\), \(19\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9792))\).

Total New Old
Modular forms 1776 160 1616
Cusp forms 1681 160 1521
Eisenstein series 95 0 95

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

\(2\)\(3\)\(17\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(16\)
\(+\)\(+\)\(-\)\(-\)\(16\)
\(+\)\(-\)\(+\)\(-\)\(26\)
\(+\)\(-\)\(-\)\(+\)\(22\)
\(-\)\(+\)\(+\)\(-\)\(16\)
\(-\)\(+\)\(-\)\(+\)\(16\)
\(-\)\(-\)\(+\)\(+\)\(22\)
\(-\)\(-\)\(-\)\(-\)\(26\)
Plus space\(+\)\(76\)
Minus space\(-\)\(84\)

Trace form

\( 160q + O(q^{10}) \) \( 160q - 16q^{13} + 160q^{25} - 16q^{29} - 32q^{37} + 160q^{49} - 64q^{53} - 16q^{61} - 16q^{77} + 32q^{89} + 32q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9792))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 17
9792.2.a.a \(1\) \(78.190\) \(\Q\) None \(0\) \(0\) \(-4\) \(-2\) \(+\) \(-\) \(-\) \(q-4q^{5}-2q^{7}+6q^{13}+q^{17}-4q^{19}+\cdots\)
9792.2.a.b \(1\) \(78.190\) \(\Q\) None \(0\) \(0\) \(-4\) \(2\) \(-\) \(-\) \(-\) \(q-4q^{5}+2q^{7}+6q^{13}+q^{17}+4q^{19}+\cdots\)
9792.2.a.c \(1\) \(78.190\) \(\Q\) None \(0\) \(0\) \(-3\) \(-4\) \(+\) \(-\) \(+\) \(q-3q^{5}-4q^{7}+q^{11}+5q^{13}-q^{17}+\cdots\)
9792.2.a.d \(1\) \(78.190\) \(\Q\) None \(0\) \(0\) \(-3\) \(-2\) \(+\) \(-\) \(-\) \(q-3q^{5}-2q^{7}+3q^{11}-3q^{13}+q^{17}+\cdots\)
9792.2.a.e \(1\) \(78.190\) \(\Q\) None \(0\) \(0\) \(-3\) \(-2\) \(-\) \(+\) \(+\) \(q-3q^{5}-2q^{7}+3q^{11}+q^{13}-q^{17}+\cdots\)
9792.2.a.f \(1\) \(78.190\) \(\Q\) None \(0\) \(0\) \(-3\) \(2\) \(+\) \(-\) \(-\) \(q-3q^{5}+2q^{7}-3q^{11}-3q^{13}+q^{17}+\cdots\)
9792.2.a.g \(1\) \(78.190\) \(\Q\) None \(0\) \(0\) \(-3\) \(2\) \(+\) \(+\) \(+\) \(q-3q^{5}+2q^{7}-3q^{11}+q^{13}-q^{17}+\cdots\)
9792.2.a.h \(1\) \(78.190\) \(\Q\) None \(0\) \(0\) \(-3\) \(4\) \(-\) \(-\) \(+\) \(q-3q^{5}+4q^{7}-q^{11}+5q^{13}-q^{17}+\cdots\)
9792.2.a.i \(1\) \(78.190\) \(\Q\) None \(0\) \(0\) \(-2\) \(-4\) \(-\) \(-\) \(+\) \(q-2q^{5}-4q^{7}+2q^{13}-q^{17}-4q^{19}+\cdots\)
9792.2.a.j \(1\) \(78.190\) \(\Q\) None \(0\) \(0\) \(-2\) \(-2\) \(+\) \(-\) \(+\) \(q-2q^{5}-2q^{7}-6q^{11}-2q^{13}-q^{17}+\cdots\)
9792.2.a.k \(1\) \(78.190\) \(\Q\) None \(0\) \(0\) \(-2\) \(0\) \(+\) \(-\) \(+\) \(q-2q^{5}-4q^{11}+2q^{13}-q^{17}-4q^{19}+\cdots\)
9792.2.a.l \(1\) \(78.190\) \(\Q\) None \(0\) \(0\) \(-2\) \(0\) \(-\) \(-\) \(+\) \(q-2q^{5}+4q^{11}+2q^{13}-q^{17}+4q^{19}+\cdots\)
9792.2.a.m \(1\) \(78.190\) \(\Q\) None \(0\) \(0\) \(-2\) \(2\) \(-\) \(-\) \(+\) \(q-2q^{5}+2q^{7}+6q^{11}-2q^{13}-q^{17}+\cdots\)
9792.2.a.n \(1\) \(78.190\) \(\Q\) None \(0\) \(0\) \(-2\) \(4\) \(+\) \(-\) \(+\) \(q-2q^{5}+4q^{7}+2q^{13}-q^{17}+4q^{19}+\cdots\)
9792.2.a.o \(1\) \(78.190\) \(\Q\) None \(0\) \(0\) \(-1\) \(-4\) \(-\) \(-\) \(-\) \(q-q^{5}-4q^{7}-3q^{11}-3q^{13}+q^{17}+\cdots\)
9792.2.a.p \(1\) \(78.190\) \(\Q\) None \(0\) \(0\) \(-1\) \(-2\) \(+\) \(+\) \(-\) \(q-q^{5}-2q^{7}-3q^{11}+5q^{13}+q^{17}+\cdots\)
9792.2.a.q \(1\) \(78.190\) \(\Q\) None \(0\) \(0\) \(-1\) \(-2\) \(-\) \(-\) \(+\) \(q-q^{5}-2q^{7}-q^{11}+q^{13}-q^{17}+\cdots\)
9792.2.a.r \(1\) \(78.190\) \(\Q\) None \(0\) \(0\) \(-1\) \(-2\) \(+\) \(+\) \(-\) \(q-q^{5}-2q^{7}+3q^{11}+q^{13}+q^{17}+\cdots\)
9792.2.a.s \(1\) \(78.190\) \(\Q\) None \(0\) \(0\) \(-1\) \(-2\) \(+\) \(-\) \(+\) \(q-q^{5}-2q^{7}+5q^{11}+5q^{13}-q^{17}+\cdots\)
9792.2.a.t \(1\) \(78.190\) \(\Q\) None \(0\) \(0\) \(-1\) \(2\) \(+\) \(-\) \(+\) \(q-q^{5}+2q^{7}-5q^{11}+5q^{13}-q^{17}+\cdots\)
9792.2.a.u \(1\) \(78.190\) \(\Q\) None \(0\) \(0\) \(-1\) \(2\) \(-\) \(+\) \(-\) \(q-q^{5}+2q^{7}-3q^{11}+q^{13}+q^{17}+\cdots\)
9792.2.a.v \(1\) \(78.190\) \(\Q\) None \(0\) \(0\) \(-1\) \(2\) \(-\) \(-\) \(+\) \(q-q^{5}+2q^{7}+q^{11}+q^{13}-q^{17}+\cdots\)
9792.2.a.w \(1\) \(78.190\) \(\Q\) None \(0\) \(0\) \(-1\) \(2\) \(-\) \(+\) \(-\) \(q-q^{5}+2q^{7}+3q^{11}+5q^{13}+q^{17}+\cdots\)
9792.2.a.x \(1\) \(78.190\) \(\Q\) None \(0\) \(0\) \(-1\) \(4\) \(+\) \(-\) \(-\) \(q-q^{5}+4q^{7}+3q^{11}-3q^{13}+q^{17}+\cdots\)
9792.2.a.y \(1\) \(78.190\) \(\Q\) None \(0\) \(0\) \(0\) \(-4\) \(+\) \(-\) \(-\) \(q-4q^{7}+6q^{11}-2q^{13}+q^{17}+4q^{19}+\cdots\)
9792.2.a.z \(1\) \(78.190\) \(\Q\) None \(0\) \(0\) \(0\) \(-2\) \(+\) \(-\) \(-\) \(q-2q^{7}-4q^{11}-2q^{13}+q^{17}+4q^{19}+\cdots\)
9792.2.a.ba \(1\) \(78.190\) \(\Q\) None \(0\) \(0\) \(0\) \(-2\) \(-\) \(-\) \(-\) \(q-2q^{7}-2q^{13}+q^{17}-4q^{19}-6q^{23}+\cdots\)
9792.2.a.bb \(1\) \(78.190\) \(\Q\) None \(0\) \(0\) \(0\) \(-2\) \(-\) \(-\) \(-\) \(q-2q^{7}-2q^{13}+q^{17}+4q^{19}+2q^{23}+\cdots\)
9792.2.a.bc \(1\) \(78.190\) \(\Q\) None \(0\) \(0\) \(0\) \(-2\) \(+\) \(-\) \(-\) \(q-2q^{7}+6q^{13}+q^{17}-4q^{19}+6q^{23}+\cdots\)
9792.2.a.bd \(1\) \(78.190\) \(\Q\) None \(0\) \(0\) \(0\) \(0\) \(-\) \(-\) \(-\) \(q-2q^{11}+6q^{13}+q^{17}+4q^{19}+4q^{23}+\cdots\)
9792.2.a.be \(1\) \(78.190\) \(\Q\) None \(0\) \(0\) \(0\) \(0\) \(+\) \(-\) \(-\) \(q+2q^{11}+6q^{13}+q^{17}-4q^{19}-4q^{23}+\cdots\)
9792.2.a.bf \(1\) \(78.190\) \(\Q\) None \(0\) \(0\) \(0\) \(2\) \(+\) \(-\) \(-\) \(q+2q^{7}-2q^{13}+q^{17}-4q^{19}-2q^{23}+\cdots\)
9792.2.a.bg \(1\) \(78.190\) \(\Q\) None \(0\) \(0\) \(0\) \(2\) \(+\) \(-\) \(-\) \(q+2q^{7}-2q^{13}+q^{17}+4q^{19}+6q^{23}+\cdots\)
9792.2.a.bh \(1\) \(78.190\) \(\Q\) None \(0\) \(0\) \(0\) \(2\) \(+\) \(-\) \(-\) \(q+2q^{7}+6q^{13}+q^{17}+4q^{19}-6q^{23}+\cdots\)
9792.2.a.bi \(1\) \(78.190\) \(\Q\) None \(0\) \(0\) \(0\) \(2\) \(+\) \(-\) \(-\) \(q+2q^{7}+4q^{11}-2q^{13}+q^{17}-4q^{19}+\cdots\)
9792.2.a.bj \(1\) \(78.190\) \(\Q\) None \(0\) \(0\) \(0\) \(4\) \(-\) \(-\) \(-\) \(q+4q^{7}-6q^{11}-2q^{13}+q^{17}-4q^{19}+\cdots\)
9792.2.a.bk \(1\) \(78.190\) \(\Q\) None \(0\) \(0\) \(1\) \(-2\) \(-\) \(-\) \(-\) \(q+q^{5}-2q^{7}-5q^{11}+q^{13}+q^{17}+\cdots\)
9792.2.a.bl \(1\) \(78.190\) \(\Q\) None \(0\) \(0\) \(1\) \(-2\) \(+\) \(+\) \(+\) \(q+q^{5}-2q^{7}-3q^{11}+q^{13}-q^{17}+\cdots\)
9792.2.a.bm \(1\) \(78.190\) \(\Q\) None \(0\) \(0\) \(1\) \(-2\) \(+\) \(+\) \(+\) \(q+q^{5}-2q^{7}+3q^{11}+5q^{13}-q^{17}+\cdots\)
9792.2.a.bn \(1\) \(78.190\) \(\Q\) None \(0\) \(0\) \(1\) \(0\) \(-\) \(-\) \(+\) \(q+q^{5}-5q^{11}+5q^{13}-q^{17}+q^{19}+\cdots\)
9792.2.a.bo \(1\) \(78.190\) \(\Q\) None \(0\) \(0\) \(1\) \(0\) \(+\) \(-\) \(+\) \(q+q^{5}+5q^{11}+5q^{13}-q^{17}-q^{19}+\cdots\)
9792.2.a.bp \(1\) \(78.190\) \(\Q\) None \(0\) \(0\) \(1\) \(2\) \(-\) \(+\) \(+\) \(q+q^{5}+2q^{7}-3q^{11}+5q^{13}-q^{17}+\cdots\)
9792.2.a.bq \(1\) \(78.190\) \(\Q\) None \(0\) \(0\) \(1\) \(2\) \(-\) \(+\) \(+\) \(q+q^{5}+2q^{7}+3q^{11}+q^{13}-q^{17}+\cdots\)
9792.2.a.br \(1\) \(78.190\) \(\Q\) None \(0\) \(0\) \(1\) \(2\) \(-\) \(-\) \(-\) \(q+q^{5}+2q^{7}+5q^{11}+q^{13}+q^{17}+\cdots\)
9792.2.a.bs \(1\) \(78.190\) \(\Q\) None \(0\) \(0\) \(2\) \(-4\) \(+\) \(-\) \(+\) \(q+2q^{5}-4q^{7}+4q^{11}-6q^{13}-q^{17}+\cdots\)
9792.2.a.bt \(1\) \(78.190\) \(\Q\) None \(0\) \(0\) \(2\) \(-2\) \(-\) \(-\) \(+\) \(q+2q^{5}-2q^{7}+2q^{11}-2q^{13}-q^{17}+\cdots\)
9792.2.a.bu \(1\) \(78.190\) \(\Q\) None \(0\) \(0\) \(2\) \(0\) \(-\) \(-\) \(+\) \(q+2q^{5}-4q^{11}+2q^{13}-q^{17}+8q^{23}+\cdots\)
9792.2.a.bv \(1\) \(78.190\) \(\Q\) None \(0\) \(0\) \(2\) \(0\) \(-\) \(-\) \(+\) \(q+2q^{5}+4q^{11}+2q^{13}-q^{17}-8q^{23}+\cdots\)
9792.2.a.bw \(1\) \(78.190\) \(\Q\) None \(0\) \(0\) \(2\) \(2\) \(-\) \(-\) \(+\) \(q+2q^{5}+2q^{7}-2q^{11}-2q^{13}-q^{17}+\cdots\)
9792.2.a.bx \(1\) \(78.190\) \(\Q\) None \(0\) \(0\) \(2\) \(4\) \(-\) \(-\) \(+\) \(q+2q^{5}+4q^{7}-4q^{11}-6q^{13}-q^{17}+\cdots\)
9792.2.a.by \(1\) \(78.190\) \(\Q\) None \(0\) \(0\) \(3\) \(-4\) \(+\) \(-\) \(-\) \(q+3q^{5}-4q^{7}-3q^{11}+q^{13}+q^{17}+\cdots\)
9792.2.a.bz \(1\) \(78.190\) \(\Q\) None \(0\) \(0\) \(3\) \(-2\) \(-\) \(+\) \(-\) \(q+3q^{5}-2q^{7}-3q^{11}+q^{13}+q^{17}+\cdots\)
9792.2.a.ca \(1\) \(78.190\) \(\Q\) None \(0\) \(0\) \(3\) \(0\) \(+\) \(-\) \(-\) \(q+3q^{5}-q^{11}-3q^{13}+q^{17}-q^{19}+\cdots\)
9792.2.a.cb \(1\) \(78.190\) \(\Q\) None \(0\) \(0\) \(3\) \(0\) \(-\) \(-\) \(-\) \(q+3q^{5}+q^{11}-3q^{13}+q^{17}+q^{19}+\cdots\)
9792.2.a.cc \(1\) \(78.190\) \(\Q\) None \(0\) \(0\) \(3\) \(2\) \(+\) \(+\) \(-\) \(q+3q^{5}+2q^{7}+3q^{11}+q^{13}+q^{17}+\cdots\)
9792.2.a.cd \(1\) \(78.190\) \(\Q\) None \(0\) \(0\) \(3\) \(4\) \(-\) \(-\) \(-\) \(q+3q^{5}+4q^{7}+3q^{11}+q^{13}+q^{17}+\cdots\)
9792.2.a.ce \(1\) \(78.190\) \(\Q\) None \(0\) \(0\) \(4\) \(-4\) \(-\) \(-\) \(-\) \(q+4q^{5}-4q^{7}+2q^{11}-2q^{13}+q^{17}+\cdots\)
9792.2.a.cf \(1\) \(78.190\) \(\Q\) None \(0\) \(0\) \(4\) \(4\) \(-\) \(-\) \(-\) \(q+4q^{5}+4q^{7}-2q^{11}-2q^{13}+q^{17}+\cdots\)
9792.2.a.cg \(2\) \(78.190\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-4\) \(0\) \(-\) \(-\) \(-\) \(q-2q^{5}-3\beta q^{7}+\beta q^{11}+4q^{13}+q^{17}+\cdots\)
9792.2.a.ch \(2\) \(78.190\) \(\Q(\sqrt{10}) \) None \(0\) \(0\) \(-4\) \(0\) \(-\) \(-\) \(-\) \(q-2q^{5}-\beta q^{7}-\beta q^{11}+4q^{13}+q^{17}+\cdots\)
9792.2.a.ci \(2\) \(78.190\) \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(-3\) \(-2\) \(-\) \(-\) \(+\) \(q+(-1-\beta )q^{5}+(-2+2\beta )q^{7}+(1-\beta )q^{11}+\cdots\)
9792.2.a.cj \(2\) \(78.190\) \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(-3\) \(2\) \(-\) \(-\) \(+\) \(q+(-1-\beta )q^{5}+(2-2\beta )q^{7}+(-1+\beta )q^{11}+\cdots\)
9792.2.a.ck \(2\) \(78.190\) \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(-2\) \(0\) \(-\) \(+\) \(+\) \(q-q^{5}+\beta q^{11}+q^{13}-q^{17}+\beta q^{19}+\cdots\)
9792.2.a.cl \(2\) \(78.190\) \(\Q(\sqrt{57}) \) None \(0\) \(0\) \(-1\) \(-8\) \(-\) \(-\) \(+\) \(q-\beta q^{5}-4q^{7}+(2-\beta )q^{11}-\beta q^{13}+\cdots\)
9792.2.a.cm \(2\) \(78.190\) \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(-1\) \(-2\) \(+\) \(-\) \(-\) \(q-\beta q^{5}+(-2+2\beta )q^{7}+(-4-\beta )q^{11}+\cdots\)
9792.2.a.cn \(2\) \(78.190\) \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(-1\) \(2\) \(-\) \(-\) \(-\) \(q-\beta q^{5}+(2-2\beta )q^{7}+(4+\beta )q^{11}+(2+\cdots)q^{13}+\cdots\)
9792.2.a.co \(2\) \(78.190\) \(\Q(\sqrt{57}) \) None \(0\) \(0\) \(-1\) \(8\) \(+\) \(-\) \(+\) \(q-\beta q^{5}+4q^{7}+(-2+\beta )q^{11}-\beta q^{13}+\cdots\)
9792.2.a.cp \(2\) \(78.190\) \(\Q(\sqrt{6}) \) None \(0\) \(0\) \(0\) \(-4\) \(-\) \(+\) \(+\) \(q+\beta q^{5}+(-2-\beta )q^{7}+2\beta q^{11}+(-2+\cdots)q^{13}+\cdots\)
9792.2.a.cq \(2\) \(78.190\) \(\Q(\sqrt{6}) \) None \(0\) \(0\) \(0\) \(-4\) \(-\) \(+\) \(-\) \(q+\beta q^{5}+(-2+\beta )q^{7}+2\beta q^{11}+(-2+\cdots)q^{13}+\cdots\)
9792.2.a.cr \(2\) \(78.190\) \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(0\) \(-2\) \(+\) \(-\) \(-\) \(q+2\beta q^{5}+(-1+\beta )q^{7}+(-3-\beta )q^{11}+\cdots\)
9792.2.a.cs \(2\) \(78.190\) \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(0\) \(2\) \(-\) \(-\) \(-\) \(q+2\beta q^{5}+(1-\beta )q^{7}+(3+\beta )q^{11}+(-2+\cdots)q^{13}+\cdots\)
9792.2.a.ct \(2\) \(78.190\) \(\Q(\sqrt{6}) \) None \(0\) \(0\) \(0\) \(4\) \(+\) \(+\) \(+\) \(q+\beta q^{5}+(2+\beta )q^{7}-2\beta q^{11}+(-2+\cdots)q^{13}+\cdots\)
9792.2.a.cu \(2\) \(78.190\) \(\Q(\sqrt{6}) \) None \(0\) \(0\) \(0\) \(4\) \(+\) \(+\) \(-\) \(q+\beta q^{5}+(2-\beta )q^{7}-2\beta q^{11}+(-2+\cdots)q^{13}+\cdots\)
9792.2.a.cv \(2\) \(78.190\) \(\Q(\sqrt{33}) \) None \(0\) \(0\) \(1\) \(-4\) \(+\) \(-\) \(-\) \(q+\beta q^{5}-2q^{7}+\beta q^{11}+(-2-\beta )q^{13}+\cdots\)
9792.2.a.cw \(2\) \(78.190\) \(\Q(\sqrt{33}) \) None \(0\) \(0\) \(1\) \(4\) \(+\) \(-\) \(-\) \(q+\beta q^{5}+2q^{7}-\beta q^{11}+(-2-\beta )q^{13}+\cdots\)
9792.2.a.cx \(2\) \(78.190\) \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(2\) \(0\) \(-\) \(+\) \(-\) \(q+q^{5}+\beta q^{11}+q^{13}+q^{17}-\beta q^{19}+\cdots\)
9792.2.a.cy \(2\) \(78.190\) \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(3\) \(0\) \(+\) \(-\) \(+\) \(q+(1+\beta )q^{5}+(-1+\beta )q^{11}+(-3+\beta )q^{13}+\cdots\)
9792.2.a.cz \(2\) \(78.190\) \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(3\) \(0\) \(-\) \(-\) \(+\) \(q+(1+\beta )q^{5}+(1-\beta )q^{11}+(-3+\beta )q^{13}+\cdots\)
9792.2.a.da \(2\) \(78.190\) \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(4\) \(-2\) \(-\) \(-\) \(+\) \(q+2q^{5}+(-1-\beta )q^{7}+(-1-\beta )q^{11}+\cdots\)
9792.2.a.db \(2\) \(78.190\) \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(4\) \(2\) \(+\) \(-\) \(+\) \(q+2q^{5}+(1-\beta )q^{7}+(1-\beta )q^{11}-2\beta q^{13}+\cdots\)
9792.2.a.dc \(3\) \(78.190\) 3.3.148.1 None \(0\) \(0\) \(-2\) \(-2\) \(+\) \(-\) \(+\) \(q+(-\beta _{1}-\beta _{2})q^{5}+(-1+\beta _{2})q^{7}+(-3+\cdots)q^{11}+\cdots\)
9792.2.a.dd \(3\) \(78.190\) 3.3.148.1 None \(0\) \(0\) \(-2\) \(2\) \(+\) \(-\) \(+\) \(q+(-\beta _{1}-\beta _{2})q^{5}+(1-\beta _{2})q^{7}+(3+\beta _{1}+\cdots)q^{11}+\cdots\)
9792.2.a.de \(3\) \(78.190\) 3.3.1304.1 None \(0\) \(0\) \(-1\) \(-2\) \(-\) \(+\) \(-\) \(q+(\beta _{1}+\beta _{2})q^{5}+(-1-\beta _{2})q^{7}+(-1+\cdots)q^{11}+\cdots\)
9792.2.a.df \(3\) \(78.190\) 3.3.1304.1 None \(0\) \(0\) \(-1\) \(2\) \(+\) \(+\) \(-\) \(q+(\beta _{1}+\beta _{2})q^{5}+(1+\beta _{2})q^{7}+(1+\beta _{1}+\cdots)q^{11}+\cdots\)
9792.2.a.dg \(3\) \(78.190\) 3.3.229.1 None \(0\) \(0\) \(1\) \(-6\) \(-\) \(-\) \(-\) \(q-\beta _{1}q^{5}-2q^{7}+(1+\beta _{1}+\beta _{2})q^{11}+\cdots\)
9792.2.a.dh \(3\) \(78.190\) 3.3.1304.1 None \(0\) \(0\) \(1\) \(-2\) \(-\) \(+\) \(+\) \(q+(-\beta _{1}-\beta _{2})q^{5}+(-1-\beta _{2})q^{7}+(1+\cdots)q^{11}+\cdots\)
9792.2.a.di \(3\) \(78.190\) 3.3.1304.1 None \(0\) \(0\) \(1\) \(2\) \(+\) \(+\) \(+\) \(q+(-\beta _{1}-\beta _{2})q^{5}+(1+\beta _{2})q^{7}+(-1+\cdots)q^{11}+\cdots\)
9792.2.a.dj \(3\) \(78.190\) 3.3.229.1 None \(0\) \(0\) \(1\) \(6\) \(-\) \(-\) \(-\) \(q-\beta _{1}q^{5}+2q^{7}+(-1-\beta _{1}-\beta _{2})q^{11}+\cdots\)
9792.2.a.dk \(3\) \(78.190\) 3.3.316.1 None \(0\) \(0\) \(3\) \(-2\) \(+\) \(-\) \(+\) \(q+(1-\beta _{1})q^{5}+(-1-\beta _{1}-\beta _{2})q^{7}+\cdots\)
9792.2.a.dl \(3\) \(78.190\) 3.3.316.1 None \(0\) \(0\) \(3\) \(2\) \(+\) \(-\) \(+\) \(q+(1-\beta _{1})q^{5}+(1+\beta _{1}+\beta _{2})q^{7}+\beta _{2}q^{11}+\cdots\)
9792.2.a.dm \(4\) \(78.190\) 4.4.13768.1 None \(0\) \(0\) \(-2\) \(-4\) \(+\) \(+\) \(+\) \(q+(-1-\beta _{2})q^{5}+(-1+\beta _{1})q^{7}+(1+\cdots)q^{11}+\cdots\)
9792.2.a.dn \(4\) \(78.190\) 4.4.13768.1 None \(0\) \(0\) \(-2\) \(4\) \(+\) \(+\) \(+\) \(q+(-1-\beta _{2})q^{5}+(1-\beta _{1})q^{7}+(-1+\cdots)q^{11}+\cdots\)
9792.2.a.do \(4\) \(78.190\) 4.4.13768.1 None \(0\) \(0\) \(2\) \(-4\) \(+\) \(+\) \(-\) \(q+(1+\beta _{2})q^{5}+(-1+\beta _{1})q^{7}+(-1+\cdots)q^{11}+\cdots\)
9792.2.a.dp \(4\) \(78.190\) 4.4.13768.1 None \(0\) \(0\) \(2\) \(4\) \(+\) \(+\) \(-\) \(q+(1+\beta _{2})q^{5}+(1-\beta _{1})q^{7}+(1+\beta _{2}+\cdots)q^{11}+\cdots\)
9792.2.a.dq \(6\) \(78.190\) 6.6.102503232.1 None \(0\) \(0\) \(-6\) \(0\) \(-\) \(+\) \(-\) \(q+(-1+\beta _{3})q^{5}+\beta _{2}q^{7}+\beta _{5}q^{11}+\cdots\)
9792.2.a.dr \(6\) \(78.190\) 6.6.102503232.1 None \(0\) \(0\) \(6\) \(0\) \(-\) \(+\) \(+\) \(q+(1-\beta _{3})q^{5}-\beta _{2}q^{7}+\beta _{5}q^{11}+(-1+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9792))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(9792)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 21}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(68))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(102))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(136))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(153))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(192))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(204))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(272))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(288))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(306))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(408))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(544))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(576))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(612))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(816))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1088))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1224))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1632))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2448))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3264))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4896))\)\(^{\oplus 2}\)