Properties

Label 8112.2.a
Level $8112$
Weight $2$
Character orbit 8112.a
Rep. character $\chi_{8112}(1,\cdot)$
Character field $\Q$
Dimension $155$
Newform subspaces $75$
Sturm bound $2912$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 8112 = 2^{4} \cdot 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8112.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 75 \)
Sturm bound: \(2912\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(5\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8112))\).

Total New Old
Modular forms 1540 155 1385
Cusp forms 1373 155 1218
Eisenstein series 167 0 167

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

\(2\)\(3\)\(13\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(18\)
\(+\)\(+\)\(-\)\(-\)\(21\)
\(+\)\(-\)\(+\)\(-\)\(23\)
\(+\)\(-\)\(-\)\(+\)\(15\)
\(-\)\(+\)\(+\)\(-\)\(18\)
\(-\)\(+\)\(-\)\(+\)\(21\)
\(-\)\(-\)\(+\)\(+\)\(18\)
\(-\)\(-\)\(-\)\(-\)\(21\)
Plus space\(+\)\(72\)
Minus space\(-\)\(83\)

Trace form

\( 155q - q^{3} + 2q^{5} - 4q^{7} + 155q^{9} + O(q^{10}) \) \( 155q - q^{3} + 2q^{5} - 4q^{7} + 155q^{9} - 4q^{11} - 2q^{15} - 2q^{17} + 8q^{23} + 149q^{25} - q^{27} + 10q^{29} - 12q^{31} - 4q^{33} + 10q^{37} + 6q^{41} - 4q^{43} + 2q^{45} - 24q^{47} + 155q^{49} - 10q^{51} + 18q^{53} + 16q^{55} - 4q^{57} + 4q^{59} + 18q^{61} - 4q^{63} - 24q^{67} + 8q^{69} + 24q^{71} - 18q^{73} + q^{75} + 16q^{77} - 24q^{79} + 155q^{81} + 44q^{83} + 4q^{85} - 6q^{87} + 6q^{89} - 8q^{93} - 16q^{95} + 6q^{97} - 4q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8112))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 13
8112.2.a.a \(1\) \(64.775\) \(\Q\) None \(0\) \(-1\) \(-4\) \(2\) \(+\) \(+\) \(-\) \(q-q^{3}-4q^{5}+2q^{7}+q^{9}-2q^{11}+\cdots\)
8112.2.a.b \(1\) \(64.775\) \(\Q\) None \(0\) \(-1\) \(-3\) \(0\) \(+\) \(+\) \(+\) \(q-q^{3}-3q^{5}+q^{9}+3q^{15}-q^{17}+\cdots\)
8112.2.a.c \(1\) \(64.775\) \(\Q\) None \(0\) \(-1\) \(-3\) \(2\) \(-\) \(+\) \(+\) \(q-q^{3}-3q^{5}+2q^{7}+q^{9}+6q^{11}+\cdots\)
8112.2.a.d \(1\) \(64.775\) \(\Q\) None \(0\) \(-1\) \(-2\) \(-4\) \(-\) \(+\) \(-\) \(q-q^{3}-2q^{5}-4q^{7}+q^{9}+6q^{11}+\cdots\)
8112.2.a.e \(1\) \(64.775\) \(\Q\) None \(0\) \(-1\) \(-2\) \(-2\) \(+\) \(+\) \(-\) \(q-q^{3}-2q^{5}-2q^{7}+q^{9}-4q^{11}+\cdots\)
8112.2.a.f \(1\) \(64.775\) \(\Q\) None \(0\) \(-1\) \(-2\) \(0\) \(+\) \(+\) \(+\) \(q-q^{3}-2q^{5}+q^{9}+2q^{15}+2q^{17}+\cdots\)
8112.2.a.g \(1\) \(64.775\) \(\Q\) None \(0\) \(-1\) \(-2\) \(2\) \(-\) \(+\) \(-\) \(q-q^{3}-2q^{5}+2q^{7}+q^{9}+2q^{15}+\cdots\)
8112.2.a.h \(1\) \(64.775\) \(\Q\) None \(0\) \(-1\) \(0\) \(0\) \(+\) \(+\) \(+\) \(q-q^{3}+q^{9}+6q^{11}+2q^{17}-4q^{23}+\cdots\)
8112.2.a.i \(1\) \(64.775\) \(\Q\) None \(0\) \(-1\) \(0\) \(2\) \(-\) \(+\) \(+\) \(q-q^{3}+2q^{7}+q^{9}-6q^{17}+2q^{19}+\cdots\)
8112.2.a.j \(1\) \(64.775\) \(\Q\) None \(0\) \(-1\) \(2\) \(-2\) \(-\) \(+\) \(-\) \(q-q^{3}+2q^{5}-2q^{7}+q^{9}-2q^{15}+\cdots\)
8112.2.a.k \(1\) \(64.775\) \(\Q\) None \(0\) \(-1\) \(2\) \(2\) \(+\) \(+\) \(-\) \(q-q^{3}+2q^{5}+2q^{7}+q^{9}+4q^{11}+\cdots\)
8112.2.a.l \(1\) \(64.775\) \(\Q\) None \(0\) \(-1\) \(2\) \(4\) \(-\) \(+\) \(-\) \(q-q^{3}+2q^{5}+4q^{7}+q^{9}-6q^{11}+\cdots\)
8112.2.a.m \(1\) \(64.775\) \(\Q\) None \(0\) \(-1\) \(3\) \(-2\) \(-\) \(+\) \(+\) \(q-q^{3}+3q^{5}-2q^{7}+q^{9}-6q^{11}+\cdots\)
8112.2.a.n \(1\) \(64.775\) \(\Q\) None \(0\) \(-1\) \(3\) \(0\) \(+\) \(+\) \(+\) \(q-q^{3}+3q^{5}+q^{9}-3q^{15}-q^{17}+\cdots\)
8112.2.a.o \(1\) \(64.775\) \(\Q\) None \(0\) \(-1\) \(4\) \(-4\) \(+\) \(+\) \(+\) \(q-q^{3}+4q^{5}-4q^{7}+q^{9}-2q^{11}+\cdots\)
8112.2.a.p \(1\) \(64.775\) \(\Q\) None \(0\) \(-1\) \(4\) \(-2\) \(+\) \(+\) \(-\) \(q-q^{3}+4q^{5}-2q^{7}+q^{9}+2q^{11}+\cdots\)
8112.2.a.q \(1\) \(64.775\) \(\Q\) None \(0\) \(1\) \(-4\) \(0\) \(+\) \(-\) \(+\) \(q+q^{3}-4q^{5}+q^{9}-2q^{11}-4q^{15}+\cdots\)
8112.2.a.r \(1\) \(64.775\) \(\Q\) None \(0\) \(1\) \(-3\) \(-4\) \(+\) \(-\) \(+\) \(q+q^{3}-3q^{5}-4q^{7}+q^{9}+4q^{11}+\cdots\)
8112.2.a.s \(1\) \(64.775\) \(\Q\) None \(0\) \(1\) \(-2\) \(-4\) \(-\) \(-\) \(+\) \(q+q^{3}-2q^{5}-4q^{7}+q^{9}+4q^{11}+\cdots\)
8112.2.a.t \(1\) \(64.775\) \(\Q\) None \(0\) \(1\) \(-2\) \(-1\) \(+\) \(-\) \(+\) \(q+q^{3}-2q^{5}-q^{7}+q^{9}+6q^{11}-2q^{15}+\cdots\)
8112.2.a.u \(1\) \(64.775\) \(\Q\) None \(0\) \(1\) \(-2\) \(1\) \(-\) \(-\) \(+\) \(q+q^{3}-2q^{5}+q^{7}+q^{9}+2q^{11}-2q^{15}+\cdots\)
8112.2.a.v \(1\) \(64.775\) \(\Q\) None \(0\) \(1\) \(-2\) \(4\) \(-\) \(-\) \(+\) \(q+q^{3}-2q^{5}+4q^{7}+q^{9}-4q^{11}+\cdots\)
8112.2.a.w \(1\) \(64.775\) \(\Q\) None \(0\) \(1\) \(-1\) \(-2\) \(-\) \(-\) \(+\) \(q+q^{3}-q^{5}-2q^{7}+q^{9}+2q^{11}-q^{15}+\cdots\)
8112.2.a.x \(1\) \(64.775\) \(\Q\) None \(0\) \(1\) \(-1\) \(2\) \(-\) \(-\) \(+\) \(q+q^{3}-q^{5}+2q^{7}+q^{9}-2q^{11}-q^{15}+\cdots\)
8112.2.a.y \(1\) \(64.775\) \(\Q\) None \(0\) \(1\) \(0\) \(-4\) \(+\) \(-\) \(+\) \(q+q^{3}-4q^{7}+q^{9}-2q^{11}-6q^{17}+\cdots\)
8112.2.a.z \(1\) \(64.775\) \(\Q\) None \(0\) \(1\) \(0\) \(-2\) \(+\) \(-\) \(-\) \(q+q^{3}-2q^{7}+q^{9}-2q^{11}-2q^{17}+\cdots\)
8112.2.a.ba \(1\) \(64.775\) \(\Q\) None \(0\) \(1\) \(0\) \(2\) \(+\) \(-\) \(-\) \(q+q^{3}+2q^{7}+q^{9}+2q^{11}-2q^{17}+\cdots\)
8112.2.a.bb \(1\) \(64.775\) \(\Q\) None \(0\) \(1\) \(1\) \(-2\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{5}-2q^{7}+q^{9}+2q^{11}+q^{15}+\cdots\)
8112.2.a.bc \(1\) \(64.775\) \(\Q\) None \(0\) \(1\) \(1\) \(2\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{5}+2q^{7}+q^{9}-2q^{11}+q^{15}+\cdots\)
8112.2.a.bd \(1\) \(64.775\) \(\Q\) None \(0\) \(1\) \(2\) \(-1\) \(-\) \(-\) \(+\) \(q+q^{3}+2q^{5}-q^{7}+q^{9}-2q^{11}+2q^{15}+\cdots\)
8112.2.a.be \(1\) \(64.775\) \(\Q\) None \(0\) \(1\) \(2\) \(0\) \(+\) \(-\) \(+\) \(q+q^{3}+2q^{5}+q^{9}+4q^{11}+2q^{15}+\cdots\)
8112.2.a.bf \(1\) \(64.775\) \(\Q\) None \(0\) \(1\) \(2\) \(1\) \(+\) \(-\) \(+\) \(q+q^{3}+2q^{5}+q^{7}+q^{9}-6q^{11}+2q^{15}+\cdots\)
8112.2.a.bg \(1\) \(64.775\) \(\Q\) None \(0\) \(1\) \(2\) \(4\) \(+\) \(-\) \(+\) \(q+q^{3}+2q^{5}+4q^{7}+q^{9}+2q^{15}+\cdots\)
8112.2.a.bh \(1\) \(64.775\) \(\Q\) None \(0\) \(1\) \(3\) \(4\) \(+\) \(-\) \(+\) \(q+q^{3}+3q^{5}+4q^{7}+q^{9}-4q^{11}+\cdots\)
8112.2.a.bi \(1\) \(64.775\) \(\Q\) None \(0\) \(1\) \(4\) \(-2\) \(-\) \(-\) \(+\) \(q+q^{3}+4q^{5}-2q^{7}+q^{9}-4q^{11}+\cdots\)
8112.2.a.bj \(2\) \(64.775\) \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(-4\) \(-2\) \(-\) \(+\) \(-\) \(q-q^{3}+(-2+\beta )q^{5}+(-1+\beta )q^{7}+\cdots\)
8112.2.a.bk \(2\) \(64.775\) \(\Q(\sqrt{17}) \) None \(0\) \(-2\) \(-3\) \(3\) \(-\) \(+\) \(+\) \(q-q^{3}+(-1-\beta )q^{5}+(2-\beta )q^{7}+q^{9}+\cdots\)
8112.2.a.bl \(2\) \(64.775\) \(\Q(\sqrt{13}) \) None \(0\) \(-2\) \(-2\) \(-2\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}+(-1+\beta )q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
8112.2.a.bm \(2\) \(64.775\) \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(0\) \(0\) \(-\) \(+\) \(+\) \(q-q^{3}+\beta q^{5}+\beta q^{7}+q^{9}-2q^{11}+\cdots\)
8112.2.a.bn \(2\) \(64.775\) \(\Q(\sqrt{13}) \) None \(0\) \(-2\) \(2\) \(2\) \(+\) \(+\) \(+\) \(q-q^{3}+q^{5}+(1+\beta )q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
8112.2.a.bo \(2\) \(64.775\) \(\Q(\sqrt{17}) \) None \(0\) \(-2\) \(3\) \(-3\) \(-\) \(+\) \(+\) \(q-q^{3}+(1+\beta )q^{5}+(-2+\beta )q^{7}+q^{9}+\cdots\)
8112.2.a.bp \(2\) \(64.775\) \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(4\) \(2\) \(-\) \(+\) \(-\) \(q-q^{3}+(2+\beta )q^{5}+(1+\beta )q^{7}+q^{9}+\cdots\)
8112.2.a.bq \(2\) \(64.775\) \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(0\) \(-6\) \(-\) \(-\) \(-\) \(q+q^{3}+\beta q^{5}+(-3+\beta )q^{7}+q^{9}+(-3+\cdots)q^{11}+\cdots\)
8112.2.a.br \(2\) \(64.775\) \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(0\) \(-2\) \(+\) \(-\) \(-\) \(q+q^{3}+\beta q^{5}+(-1-\beta )q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
8112.2.a.bs \(2\) \(64.775\) \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(0\) \(0\) \(-\) \(-\) \(-\) \(q+q^{3}+\beta q^{5}+q^{9}+\beta q^{11}+\beta q^{15}+\cdots\)
8112.2.a.bt \(2\) \(64.775\) \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(0\) \(0\) \(-\) \(-\) \(-\) \(q+q^{3}+\beta q^{5}+2\beta q^{7}+q^{9}-2\beta q^{11}+\cdots\)
8112.2.a.bu \(2\) \(64.775\) \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(0\) \(0\) \(-\) \(-\) \(-\) \(q+q^{3}+2\beta q^{5}-\beta q^{7}+q^{9}+2\beta q^{11}+\cdots\)
8112.2.a.bv \(2\) \(64.775\) \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(0\) \(0\) \(-\) \(-\) \(-\) \(q+q^{3}-\beta q^{7}+q^{9}-\beta q^{11}+6q^{17}+\cdots\)
8112.2.a.bw \(2\) \(64.775\) \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(0\) \(2\) \(+\) \(-\) \(-\) \(q+q^{3}+\beta q^{5}+(1-\beta )q^{7}+q^{9}+(1-\beta )q^{11}+\cdots\)
8112.2.a.bx \(2\) \(64.775\) \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(0\) \(6\) \(-\) \(-\) \(-\) \(q+q^{3}+\beta q^{5}+(3+\beta )q^{7}+q^{9}+(3+\beta )q^{11}+\cdots\)
8112.2.a.by \(3\) \(64.775\) \(\Q(\zeta_{14})^+\) None \(0\) \(-3\) \(-4\) \(10\) \(-\) \(+\) \(-\) \(q-q^{3}+(-1-\beta _{1})q^{5}+(3+\beta _{1})q^{7}+\cdots\)
8112.2.a.bz \(3\) \(64.775\) \(\Q(\zeta_{14})^+\) None \(0\) \(-3\) \(-3\) \(-3\) \(-\) \(+\) \(-\) \(q-q^{3}+(-1-\beta _{1}-\beta _{2})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
8112.2.a.ca \(3\) \(64.775\) \(\Q(\zeta_{14})^+\) None \(0\) \(-3\) \(0\) \(-6\) \(-\) \(+\) \(-\) \(q-q^{3}+(-\beta _{1}-\beta _{2})q^{5}+(-2-\beta _{1}+\cdots)q^{7}+\cdots\)
8112.2.a.cb \(3\) \(64.775\) \(\Q(\zeta_{14})^+\) None \(0\) \(-3\) \(0\) \(0\) \(+\) \(+\) \(+\) \(q-q^{3}+(-\beta _{1}-\beta _{2})q^{5}+(-\beta _{1}-\beta _{2})q^{7}+\cdots\)
8112.2.a.cc \(3\) \(64.775\) \(\Q(\zeta_{14})^+\) None \(0\) \(-3\) \(0\) \(0\) \(+\) \(+\) \(-\) \(q-q^{3}+(1-2\beta _{1}+\beta _{2})q^{5}+(1-2\beta _{1}+\cdots)q^{7}+\cdots\)
8112.2.a.cd \(3\) \(64.775\) \(\Q(\zeta_{14})^+\) None \(0\) \(-3\) \(0\) \(6\) \(-\) \(+\) \(+\) \(q-q^{3}+(1-2\beta _{1}+\beta _{2})q^{5}+(3-2\beta _{1}+\cdots)q^{7}+\cdots\)
8112.2.a.ce \(3\) \(64.775\) \(\Q(\zeta_{14})^+\) None \(0\) \(-3\) \(3\) \(3\) \(-\) \(+\) \(+\) \(q-q^{3}+(1+\beta _{1}+\beta _{2})q^{5}+(\beta _{1}-2\beta _{2})q^{7}+\cdots\)
8112.2.a.cf \(3\) \(64.775\) \(\Q(\zeta_{14})^+\) None \(0\) \(-3\) \(4\) \(-10\) \(-\) \(+\) \(+\) \(q-q^{3}+(1+\beta _{1})q^{5}+(-3-\beta _{1})q^{7}+\cdots\)
8112.2.a.cg \(3\) \(64.775\) \(\Q(\zeta_{14})^+\) None \(0\) \(3\) \(-6\) \(2\) \(-\) \(-\) \(+\) \(q+q^{3}+(-2+\beta _{1}+\beta _{2})q^{5}+(\beta _{1}-\beta _{2})q^{7}+\cdots\)
8112.2.a.ch \(3\) \(64.775\) \(\Q(\zeta_{14})^+\) None \(0\) \(3\) \(-2\) \(-6\) \(-\) \(-\) \(+\) \(q+q^{3}+(-1-\beta _{2})q^{5}+(-1-2\beta _{1}+\cdots)q^{7}+\cdots\)
8112.2.a.ci \(3\) \(64.775\) \(\Q(\zeta_{14})^+\) None \(0\) \(3\) \(-2\) \(0\) \(+\) \(-\) \(-\) \(q+q^{3}+(-1-\beta _{2})q^{5}+(1-2\beta _{1}+\beta _{2})q^{7}+\cdots\)
8112.2.a.cj \(3\) \(64.775\) \(\Q(\zeta_{14})^+\) None \(0\) \(3\) \(-1\) \(9\) \(-\) \(-\) \(-\) \(q+q^{3}+(1-3\beta _{1}+\beta _{2})q^{5}+(4-\beta _{1}+\cdots)q^{7}+\cdots\)
8112.2.a.ck \(3\) \(64.775\) 3.3.837.1 None \(0\) \(3\) \(0\) \(-3\) \(+\) \(-\) \(+\) \(q+q^{3}-\beta _{2}q^{5}+(-1+\beta _{1})q^{7}+q^{9}+\cdots\)
8112.2.a.cl \(3\) \(64.775\) 3.3.837.1 None \(0\) \(3\) \(0\) \(3\) \(+\) \(-\) \(+\) \(q+q^{3}+\beta _{2}q^{5}+(1-\beta _{1})q^{7}+q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots\)
8112.2.a.cm \(3\) \(64.775\) \(\Q(\zeta_{14})^+\) None \(0\) \(3\) \(1\) \(-9\) \(-\) \(-\) \(+\) \(q+q^{3}+(-\beta _{1}-2\beta _{2})q^{5}+(-2-2\beta _{1}+\cdots)q^{7}+\cdots\)
8112.2.a.cn \(3\) \(64.775\) \(\Q(\zeta_{14})^+\) None \(0\) \(3\) \(2\) \(0\) \(+\) \(-\) \(+\) \(q+q^{3}+(1-\beta _{1})q^{5}+(1-\beta _{1}+2\beta _{2})q^{7}+\cdots\)
8112.2.a.co \(3\) \(64.775\) \(\Q(\zeta_{14})^+\) None \(0\) \(3\) \(2\) \(6\) \(-\) \(-\) \(-\) \(q+q^{3}+(1-\beta _{1})q^{5}+(3-\beta _{1}+2\beta _{2})q^{7}+\cdots\)
8112.2.a.cp \(3\) \(64.775\) \(\Q(\zeta_{14})^+\) None \(0\) \(3\) \(6\) \(-2\) \(-\) \(-\) \(-\) \(q+q^{3}+(2-\beta _{1}-\beta _{2})q^{5}+(-\beta _{1}+\beta _{2})q^{7}+\cdots\)
8112.2.a.cq \(4\) \(64.775\) 4.4.25488.1 None \(0\) \(-4\) \(-4\) \(2\) \(+\) \(+\) \(-\) \(q-q^{3}+(-1+\beta _{1}-\beta _{2})q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)
8112.2.a.cr \(4\) \(64.775\) \(\Q(\sqrt{3}, \sqrt{43})\) None \(0\) \(-4\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q-q^{3}+\beta _{1}q^{5}+(-\beta _{1}+\beta _{2})q^{7}+q^{9}+\cdots\)
8112.2.a.cs \(4\) \(64.775\) 4.4.25488.1 None \(0\) \(-4\) \(4\) \(-2\) \(+\) \(+\) \(-\) \(q-q^{3}+(1-\beta _{1}+\beta _{2})q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
8112.2.a.ct \(6\) \(64.775\) 6.6.27700337.1 None \(0\) \(-6\) \(-1\) \(-5\) \(+\) \(+\) \(+\) \(q-q^{3}+(\beta _{1}-\beta _{3})q^{5}+(-1+\beta _{2}+\beta _{4}+\cdots)q^{7}+\cdots\)
8112.2.a.cu \(6\) \(64.775\) 6.6.27700337.1 None \(0\) \(-6\) \(1\) \(5\) \(+\) \(+\) \(-\) \(q-q^{3}+(-\beta _{1}+\beta _{3})q^{5}+(1-\beta _{2}-\beta _{4}+\cdots)q^{7}+\cdots\)
8112.2.a.cv \(6\) \(64.775\) 6.6.27700337.1 None \(0\) \(6\) \(-1\) \(7\) \(+\) \(-\) \(+\) \(q+q^{3}-\beta _{5}q^{5}+(1+\beta _{1})q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
8112.2.a.cw \(6\) \(64.775\) 6.6.27700337.1 None \(0\) \(6\) \(1\) \(-7\) \(+\) \(-\) \(-\) \(q+q^{3}+\beta _{5}q^{5}+(-1-\beta _{1})q^{7}+q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8112))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8112)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(104))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(156))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(169))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(208))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(312))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(338))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(507))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(624))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(676))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1014))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1352))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2028))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2704))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4056))\)\(^{\oplus 2}\)