Properties

Label 7488.2.a
Level $7488$
Weight $2$
Character orbit 7488.a
Rep. character $\chi_{7488}(1,\cdot)$
Character field $\Q$
Dimension $120$
Newform subspaces $82$
Sturm bound $2688$
Trace bound $29$

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Defining parameters

Level: \( N \) \(=\) \( 7488 = 2^{6} \cdot 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7488.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 82 \)
Sturm bound: \(2688\)
Trace bound: \(29\)
Distinguishing \(T_p\): \(5\), \(7\), \(11\), \(17\), \(19\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7488))\).

Total New Old
Modular forms 1392 120 1272
Cusp forms 1297 120 1177
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.

\(2\)\(3\)\(13\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(10\)
\(+\)\(+\)\(-\)\(-\)\(14\)
\(+\)\(-\)\(+\)\(-\)\(19\)
\(+\)\(-\)\(-\)\(+\)\(17\)
\(-\)\(+\)\(+\)\(-\)\(14\)
\(-\)\(+\)\(-\)\(+\)\(10\)
\(-\)\(-\)\(+\)\(+\)\(17\)
\(-\)\(-\)\(-\)\(-\)\(19\)
Plus space\(+\)\(54\)
Minus space\(-\)\(66\)

Trace form

\( 120q + O(q^{10}) \) \( 120q + 120q^{25} - 16q^{29} - 16q^{37} + 16q^{41} + 120q^{49} - 64q^{53} + 32q^{61} + 32q^{77} + 80q^{85} + 32q^{89} + 32q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7488))\) 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
7488.2.a.a \(1\) \(59.792\) \(\Q\) None \(0\) \(0\) \(-4\) \(-4\) \(-\) \(+\) \(-\) \(q-4q^{5}-4q^{7}-4q^{11}+q^{13}+8q^{23}+\cdots\)
7488.2.a.b \(1\) \(59.792\) \(\Q\) None \(0\) \(0\) \(-4\) \(-4\) \(+\) \(-\) \(-\) \(q-4q^{5}-4q^{7}-2q^{11}+q^{13}+6q^{17}+\cdots\)
7488.2.a.c \(1\) \(59.792\) \(\Q\) None \(0\) \(0\) \(-4\) \(-2\) \(+\) \(-\) \(+\) \(q-4q^{5}-2q^{7}-4q^{11}-q^{13}-2q^{17}+\cdots\)
7488.2.a.d \(1\) \(59.792\) \(\Q\) None \(0\) \(0\) \(-4\) \(2\) \(-\) \(-\) \(+\) \(q-4q^{5}+2q^{7}+4q^{11}-q^{13}-2q^{17}+\cdots\)
7488.2.a.e \(1\) \(59.792\) \(\Q\) None \(0\) \(0\) \(-4\) \(4\) \(-\) \(-\) \(-\) \(q-4q^{5}+4q^{7}+2q^{11}+q^{13}+6q^{17}+\cdots\)
7488.2.a.f \(1\) \(59.792\) \(\Q\) None \(0\) \(0\) \(-4\) \(4\) \(+\) \(+\) \(-\) \(q-4q^{5}+4q^{7}+4q^{11}+q^{13}-8q^{23}+\cdots\)
7488.2.a.g \(1\) \(59.792\) \(\Q\) None \(0\) \(0\) \(-3\) \(-1\) \(+\) \(-\) \(+\) \(q-3q^{5}-q^{7}+6q^{11}-q^{13}+3q^{17}+\cdots\)
7488.2.a.h \(1\) \(59.792\) \(\Q\) None \(0\) \(0\) \(-3\) \(1\) \(-\) \(-\) \(+\) \(q-3q^{5}+q^{7}-6q^{11}-q^{13}+3q^{17}+\cdots\)
7488.2.a.i \(1\) \(59.792\) \(\Q\) None \(0\) \(0\) \(-2\) \(-4\) \(-\) \(-\) \(+\) \(q-2q^{5}-4q^{7}-q^{13}-2q^{17}+8q^{19}+\cdots\)
7488.2.a.j \(1\) \(59.792\) \(\Q\) None \(0\) \(0\) \(-2\) \(-2\) \(+\) \(+\) \(-\) \(q-2q^{5}-2q^{7}-4q^{11}+q^{13}+6q^{19}+\cdots\)
7488.2.a.k \(1\) \(59.792\) \(\Q\) None \(0\) \(0\) \(-2\) \(-2\) \(-\) \(+\) \(-\) \(q-2q^{5}-2q^{7}+4q^{11}+q^{13}-2q^{19}+\cdots\)
7488.2.a.l \(1\) \(59.792\) \(\Q\) None \(0\) \(0\) \(-2\) \(-2\) \(+\) \(-\) \(-\) \(q-2q^{5}-2q^{7}+6q^{11}+q^{13}+2q^{17}+\cdots\)
7488.2.a.m \(1\) \(59.792\) \(\Q\) None \(0\) \(0\) \(-2\) \(0\) \(+\) \(-\) \(+\) \(q-2q^{5}-4q^{11}-q^{13}+6q^{17}-8q^{19}+\cdots\)
7488.2.a.n \(1\) \(59.792\) \(\Q\) None \(0\) \(0\) \(-2\) \(0\) \(+\) \(+\) \(+\) \(q-2q^{5}-2q^{11}-q^{13}-4q^{19}+4q^{23}+\cdots\)
7488.2.a.o \(1\) \(59.792\) \(\Q\) None \(0\) \(0\) \(-2\) \(0\) \(+\) \(+\) \(+\) \(q-2q^{5}+2q^{11}-q^{13}+4q^{19}-4q^{23}+\cdots\)
7488.2.a.p \(1\) \(59.792\) \(\Q\) None \(0\) \(0\) \(-2\) \(0\) \(+\) \(-\) \(+\) \(q-2q^{5}+4q^{11}-q^{13}+6q^{17}+8q^{19}+\cdots\)
7488.2.a.q \(1\) \(59.792\) \(\Q\) None \(0\) \(0\) \(-2\) \(2\) \(+\) \(-\) \(-\) \(q-2q^{5}+2q^{7}-6q^{11}+q^{13}+2q^{17}+\cdots\)
7488.2.a.r \(1\) \(59.792\) \(\Q\) None \(0\) \(0\) \(-2\) \(2\) \(+\) \(+\) \(-\) \(q-2q^{5}+2q^{7}-4q^{11}+q^{13}+2q^{19}+\cdots\)
7488.2.a.s \(1\) \(59.792\) \(\Q\) None \(0\) \(0\) \(-2\) \(2\) \(-\) \(+\) \(-\) \(q-2q^{5}+2q^{7}+4q^{11}+q^{13}-6q^{19}+\cdots\)
7488.2.a.t \(1\) \(59.792\) \(\Q\) None \(0\) \(0\) \(-2\) \(4\) \(+\) \(-\) \(+\) \(q-2q^{5}+4q^{7}-q^{13}-2q^{17}-8q^{19}+\cdots\)
7488.2.a.u \(1\) \(59.792\) \(\Q\) None \(0\) \(0\) \(-1\) \(-5\) \(-\) \(-\) \(-\) \(q-q^{5}-5q^{7}+2q^{11}+q^{13}+3q^{17}+\cdots\)
7488.2.a.v \(1\) \(59.792\) \(\Q\) None \(0\) \(0\) \(-1\) \(-1\) \(-\) \(-\) \(-\) \(q-q^{5}-q^{7}+2q^{11}+q^{13}+3q^{17}+\cdots\)
7488.2.a.w \(1\) \(59.792\) \(\Q\) None \(0\) \(0\) \(-1\) \(1\) \(+\) \(-\) \(-\) \(q-q^{5}+q^{7}-2q^{11}+q^{13}+3q^{17}+\cdots\)
7488.2.a.x \(1\) \(59.792\) \(\Q\) None \(0\) \(0\) \(-1\) \(5\) \(+\) \(-\) \(-\) \(q-q^{5}+5q^{7}-2q^{11}+q^{13}+3q^{17}+\cdots\)
7488.2.a.y \(1\) \(59.792\) \(\Q\) None \(0\) \(0\) \(0\) \(-4\) \(+\) \(-\) \(-\) \(q-4q^{7}-2q^{11}+q^{13}+6q^{17}+4q^{19}+\cdots\)
7488.2.a.z \(1\) \(59.792\) \(\Q\) None \(0\) \(0\) \(0\) \(-2\) \(-\) \(-\) \(+\) \(q-2q^{7}-4q^{11}-q^{13}+6q^{17}+6q^{19}+\cdots\)
7488.2.a.ba \(1\) \(59.792\) \(\Q\) None \(0\) \(0\) \(0\) \(-2\) \(-\) \(-\) \(+\) \(q-2q^{7}-q^{13}-2q^{17}-2q^{19}+8q^{23}+\cdots\)
7488.2.a.bb \(1\) \(59.792\) \(\Q\) None \(0\) \(0\) \(0\) \(-2\) \(-\) \(-\) \(+\) \(q-2q^{7}-q^{13}+6q^{17}+2q^{19}-5q^{25}+\cdots\)
7488.2.a.bc \(1\) \(59.792\) \(\Q\) None \(0\) \(0\) \(0\) \(0\) \(-\) \(-\) \(-\) \(q-6q^{11}+q^{13}-2q^{17}+4q^{23}-5q^{25}+\cdots\)
7488.2.a.bd \(1\) \(59.792\) \(\Q\) None \(0\) \(0\) \(0\) \(0\) \(+\) \(-\) \(-\) \(q+6q^{11}+q^{13}-2q^{17}-4q^{23}-5q^{25}+\cdots\)
7488.2.a.be \(1\) \(59.792\) \(\Q\) None \(0\) \(0\) \(0\) \(2\) \(-\) \(-\) \(+\) \(q+2q^{7}-q^{13}-2q^{17}+2q^{19}-8q^{23}+\cdots\)
7488.2.a.bf \(1\) \(59.792\) \(\Q\) None \(0\) \(0\) \(0\) \(2\) \(+\) \(-\) \(+\) \(q+2q^{7}-q^{13}+6q^{17}-2q^{19}-5q^{25}+\cdots\)
7488.2.a.bg \(1\) \(59.792\) \(\Q\) None \(0\) \(0\) \(0\) \(2\) \(-\) \(-\) \(+\) \(q+2q^{7}+4q^{11}-q^{13}+6q^{17}-6q^{19}+\cdots\)
7488.2.a.bh \(1\) \(59.792\) \(\Q\) None \(0\) \(0\) \(0\) \(4\) \(-\) \(-\) \(-\) \(q+4q^{7}+2q^{11}+q^{13}+6q^{17}-4q^{19}+\cdots\)
7488.2.a.bi \(1\) \(59.792\) \(\Q\) None \(0\) \(0\) \(1\) \(-3\) \(+\) \(-\) \(+\) \(q+q^{5}-3q^{7}-2q^{11}-q^{13}+3q^{17}+\cdots\)
7488.2.a.bj \(1\) \(59.792\) \(\Q\) None \(0\) \(0\) \(1\) \(3\) \(+\) \(-\) \(+\) \(q+q^{5}+3q^{7}+2q^{11}-q^{13}+3q^{17}+\cdots\)
7488.2.a.bk \(1\) \(59.792\) \(\Q\) None \(0\) \(0\) \(2\) \(-4\) \(-\) \(-\) \(+\) \(q+2q^{5}-4q^{7}+4q^{11}-q^{13}-2q^{17}+\cdots\)
7488.2.a.bl \(1\) \(59.792\) \(\Q\) None \(0\) \(0\) \(2\) \(-4\) \(+\) \(-\) \(+\) \(q+2q^{5}-4q^{7}+4q^{11}-q^{13}-2q^{17}+\cdots\)
7488.2.a.bm \(1\) \(59.792\) \(\Q\) None \(0\) \(0\) \(2\) \(-2\) \(-\) \(+\) \(-\) \(q+2q^{5}-2q^{7}-4q^{11}+q^{13}-2q^{19}+\cdots\)
7488.2.a.bn \(1\) \(59.792\) \(\Q\) None \(0\) \(0\) \(2\) \(-2\) \(+\) \(-\) \(-\) \(q+2q^{5}-2q^{7}-2q^{11}+q^{13}-6q^{17}+\cdots\)
7488.2.a.bo \(1\) \(59.792\) \(\Q\) None \(0\) \(0\) \(2\) \(-2\) \(+\) \(-\) \(-\) \(q+2q^{5}-2q^{7}+2q^{11}+q^{13}-6q^{17}+\cdots\)
7488.2.a.bp \(1\) \(59.792\) \(\Q\) None \(0\) \(0\) \(2\) \(-2\) \(+\) \(+\) \(-\) \(q+2q^{5}-2q^{7}+4q^{11}+q^{13}+6q^{19}+\cdots\)
7488.2.a.bq \(1\) \(59.792\) \(\Q\) None \(0\) \(0\) \(2\) \(0\) \(+\) \(+\) \(+\) \(q+2q^{5}-2q^{11}-q^{13}+4q^{19}+4q^{23}+\cdots\)
7488.2.a.br \(1\) \(59.792\) \(\Q\) None \(0\) \(0\) \(2\) \(0\) \(-\) \(-\) \(+\) \(q+2q^{5}-q^{13}-2q^{17}-4q^{19}-q^{25}+\cdots\)
7488.2.a.bs \(1\) \(59.792\) \(\Q\) None \(0\) \(0\) \(2\) \(0\) \(+\) \(-\) \(+\) \(q+2q^{5}-q^{13}-2q^{17}+4q^{19}-q^{25}+\cdots\)
7488.2.a.bt \(1\) \(59.792\) \(\Q\) None \(0\) \(0\) \(2\) \(0\) \(+\) \(+\) \(+\) \(q+2q^{5}+2q^{11}-q^{13}-4q^{19}-4q^{23}+\cdots\)
7488.2.a.bu \(1\) \(59.792\) \(\Q\) None \(0\) \(0\) \(2\) \(2\) \(-\) \(+\) \(-\) \(q+2q^{5}+2q^{7}-4q^{11}+q^{13}-6q^{19}+\cdots\)
7488.2.a.bv \(1\) \(59.792\) \(\Q\) None \(0\) \(0\) \(2\) \(2\) \(+\) \(-\) \(-\) \(q+2q^{5}+2q^{7}-2q^{11}+q^{13}-6q^{17}+\cdots\)
7488.2.a.bw \(1\) \(59.792\) \(\Q\) None \(0\) \(0\) \(2\) \(2\) \(-\) \(-\) \(-\) \(q+2q^{5}+2q^{7}+2q^{11}+q^{13}-6q^{17}+\cdots\)
7488.2.a.bx \(1\) \(59.792\) \(\Q\) None \(0\) \(0\) \(2\) \(2\) \(+\) \(+\) \(-\) \(q+2q^{5}+2q^{7}+4q^{11}+q^{13}+2q^{19}+\cdots\)
7488.2.a.by \(1\) \(59.792\) \(\Q\) None \(0\) \(0\) \(2\) \(4\) \(-\) \(-\) \(+\) \(q+2q^{5}+4q^{7}-4q^{11}-q^{13}-2q^{17}+\cdots\)
7488.2.a.bz \(1\) \(59.792\) \(\Q\) None \(0\) \(0\) \(2\) \(4\) \(+\) \(-\) \(+\) \(q+2q^{5}+4q^{7}-4q^{11}-q^{13}-2q^{17}+\cdots\)
7488.2.a.ca \(1\) \(59.792\) \(\Q\) None \(0\) \(0\) \(4\) \(-4\) \(-\) \(+\) \(-\) \(q+4q^{5}-4q^{7}+4q^{11}+q^{13}-8q^{23}+\cdots\)
7488.2.a.cb \(1\) \(59.792\) \(\Q\) None \(0\) \(0\) \(4\) \(0\) \(+\) \(-\) \(-\) \(q+4q^{5}-2q^{11}+q^{13}-2q^{17}-8q^{19}+\cdots\)
7488.2.a.cc \(1\) \(59.792\) \(\Q\) None \(0\) \(0\) \(4\) \(0\) \(-\) \(-\) \(-\) \(q+4q^{5}+2q^{11}+q^{13}-2q^{17}+8q^{19}+\cdots\)
7488.2.a.cd \(1\) \(59.792\) \(\Q\) None \(0\) \(0\) \(4\) \(4\) \(+\) \(+\) \(-\) \(q+4q^{5}+4q^{7}-4q^{11}+q^{13}+8q^{23}+\cdots\)
7488.2.a.ce \(2\) \(59.792\) \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(-3\) \(-3\) \(+\) \(-\) \(-\) \(q+(-1-\beta )q^{5}+(-1-\beta )q^{7}-2q^{11}+\cdots\)
7488.2.a.cf \(2\) \(59.792\) \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(-3\) \(3\) \(+\) \(-\) \(-\) \(q+(-1-\beta )q^{5}+(1+\beta )q^{7}+2q^{11}+\cdots\)
7488.2.a.cg \(2\) \(59.792\) \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(-2\) \(-6\) \(-\) \(-\) \(-\) \(q+(-1-\beta )q^{5}+(-3+\beta )q^{7}+2\beta q^{11}+\cdots\)
7488.2.a.ch \(2\) \(59.792\) \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(-2\) \(6\) \(-\) \(-\) \(-\) \(q+(-1-\beta )q^{5}+(3-\beta )q^{7}-2\beta q^{11}+\cdots\)
7488.2.a.ci \(2\) \(59.792\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(-4\) \(+\) \(+\) \(+\) \(q+\beta q^{5}+(-2-\beta )q^{7}+(-2-\beta )q^{11}+\cdots\)
7488.2.a.cj \(2\) \(59.792\) \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(0\) \(-4\) \(-\) \(+\) \(+\) \(q-2q^{7}-\beta q^{11}-q^{13}-2\beta q^{17}+2q^{19}+\cdots\)
7488.2.a.ck \(2\) \(59.792\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(-4\) \(+\) \(+\) \(+\) \(q+\beta q^{5}+(-2+\beta )q^{7}+(2-\beta )q^{11}+\cdots\)
7488.2.a.cl \(2\) \(59.792\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) \(+\) \(-\) \(-\) \(q+\beta q^{5}-\beta q^{7}-2q^{11}+q^{13}+(-2+\cdots)q^{17}+\cdots\)
7488.2.a.cm \(2\) \(59.792\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q-\beta q^{7}+\beta q^{11}+q^{13}+\beta q^{19}-2\beta q^{23}+\cdots\)
7488.2.a.cn \(2\) \(59.792\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q+\beta q^{7}+\beta q^{11}+q^{13}-\beta q^{19}-2\beta q^{23}+\cdots\)
7488.2.a.co \(2\) \(59.792\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) \(-\) \(-\) \(-\) \(q+\beta q^{5}+\beta q^{7}+2q^{11}+q^{13}+(-2+\cdots)q^{17}+\cdots\)
7488.2.a.cp \(2\) \(59.792\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(4\) \(-\) \(+\) \(+\) \(q+\beta q^{5}+(2-\beta )q^{7}+(-2+\beta )q^{11}+\cdots\)
7488.2.a.cq \(2\) \(59.792\) \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(0\) \(4\) \(+\) \(+\) \(+\) \(q+2q^{7}-\beta q^{11}-q^{13}+2\beta q^{17}-2q^{19}+\cdots\)
7488.2.a.cr \(2\) \(59.792\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(4\) \(-\) \(+\) \(+\) \(q+\beta q^{5}+(2+\beta )q^{7}+(2+\beta )q^{11}-q^{13}+\cdots\)
7488.2.a.cs \(2\) \(59.792\) \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(2\) \(-2\) \(-\) \(-\) \(-\) \(q+(1+\beta )q^{5}+(-1-\beta )q^{7}-2q^{11}+\cdots\)
7488.2.a.ct \(2\) \(59.792\) \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(2\) \(2\) \(-\) \(-\) \(-\) \(q+(1+\beta )q^{5}+(1+\beta )q^{7}+2q^{11}+q^{13}+\cdots\)
7488.2.a.cu \(2\) \(59.792\) \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(3\) \(-1\) \(+\) \(-\) \(+\) \(q+(1+\beta )q^{5}+(-1+\beta )q^{7}+(-2+2\beta )q^{11}+\cdots\)
7488.2.a.cv \(2\) \(59.792\) \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(3\) \(1\) \(-\) \(-\) \(+\) \(q+(1+\beta )q^{5}+(1-\beta )q^{7}+(2-2\beta )q^{11}+\cdots\)
7488.2.a.cw \(2\) \(59.792\) \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(6\) \(0\) \(-\) \(-\) \(-\) \(q+3q^{5}+\beta q^{7}-2\beta q^{11}+q^{13}+3q^{17}+\cdots\)
7488.2.a.cx \(3\) \(59.792\) 3.3.148.1 None \(0\) \(0\) \(2\) \(0\) \(+\) \(-\) \(+\) \(q+(1+\beta _{1})q^{5}+\beta _{2}q^{7}+(-1+\beta _{1}+\beta _{2})q^{11}+\cdots\)
7488.2.a.cy \(3\) \(59.792\) 3.3.148.1 None \(0\) \(0\) \(2\) \(0\) \(+\) \(-\) \(+\) \(q+(1+\beta _{1})q^{5}-\beta _{2}q^{7}+(1-\beta _{1}-\beta _{2})q^{11}+\cdots\)
7488.2.a.cz \(4\) \(59.792\) \(\Q(\zeta_{20})^+\) None \(0\) \(0\) \(-4\) \(0\) \(-\) \(+\) \(+\) \(q+(-1+\beta _{3})q^{5}-\beta _{2}q^{7}+(\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots\)
7488.2.a.da \(4\) \(59.792\) 4.4.13448.1 None \(0\) \(0\) \(-2\) \(0\) \(-\) \(-\) \(+\) \(q+\beta _{3}q^{5}+(-\beta _{1}+\beta _{2})q^{7}+\beta _{1}q^{11}+\cdots\)
7488.2.a.db \(4\) \(59.792\) \(\Q(\zeta_{24})^+\) None \(0\) \(0\) \(0\) \(0\) \(+\) \(+\) \(-\) \(q+\beta _{1}q^{5}+\beta _{3}q^{7}+(-2-\beta _{2})q^{11}+\cdots\)
7488.2.a.dc \(4\) \(59.792\) \(\Q(\zeta_{24})^+\) None \(0\) \(0\) \(0\) \(0\) \(+\) \(+\) \(-\) \(q+\beta _{1}q^{5}-\beta _{3}q^{7}+(2+\beta _{2})q^{11}+q^{13}+\cdots\)
7488.2.a.dd \(4\) \(59.792\) \(\Q(\zeta_{20})^+\) None \(0\) \(0\) \(4\) \(0\) \(-\) \(+\) \(+\) \(q+(1-\beta _{3})q^{5}-\beta _{2}q^{7}+(-\beta _{1}-\beta _{2}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7488))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(7488)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(104))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(117))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(156))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(192))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(208))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(234))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(288))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(312))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(416))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(468))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(576))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(624))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(832))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(936))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1248))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1872))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2496))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3744))\)\(^{\oplus 2}\)