Properties

Label 7623.2.a
Level 7623
Weight 2
Character orbit a
Rep. character \(\chi_{7623}(1,\cdot)\)
Character field \(\Q\)
Dimension 273
Newforms 81
Sturm bound 2112
Trace bound 13

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Defining parameters

Level: \( N \) = \( 7623 = 3^{2} \cdot 7 \cdot 11^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 7623.a (trivial)
Character field: \(\Q\)
Newforms: \( 81 \)
Sturm bound: \(2112\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(2\), \(5\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7623))\).

Total New Old
Modular forms 1104 273 831
Cusp forms 1009 273 736
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.

\(3\)\(7\)\(11\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(26\)
\(+\)\(+\)\(-\)\(-\)\(30\)
\(+\)\(-\)\(+\)\(-\)\(34\)
\(+\)\(-\)\(-\)\(+\)\(20\)
\(-\)\(+\)\(+\)\(-\)\(41\)
\(-\)\(+\)\(-\)\(+\)\(40\)
\(-\)\(-\)\(+\)\(+\)\(37\)
\(-\)\(-\)\(-\)\(-\)\(45\)
Plus space\(+\)\(123\)
Minus space\(-\)\(150\)

Trace form

\( 273q + q^{2} + 269q^{4} + 6q^{5} - q^{7} - 3q^{8} + O(q^{10}) \) \( 273q + q^{2} + 269q^{4} + 6q^{5} - q^{7} - 3q^{8} + 6q^{10} + 6q^{13} - 3q^{14} + 269q^{16} + 14q^{17} - 8q^{19} - 6q^{20} - 12q^{23} + 287q^{25} + 2q^{26} - 3q^{28} + 22q^{29} - 8q^{31} - 35q^{32} + 2q^{34} + 6q^{35} + 6q^{37} - 24q^{38} + 6q^{40} + 22q^{41} + 12q^{43} + 20q^{46} - 12q^{47} + 273q^{49} - 65q^{50} + 50q^{52} + 10q^{53} - 15q^{56} + 34q^{58} - 8q^{59} + 18q^{61} + 4q^{62} + 309q^{64} + 20q^{65} + 4q^{67} + 30q^{68} + 18q^{70} - 2q^{73} + 22q^{74} + 36q^{76} - 36q^{79} + 22q^{80} + 38q^{82} + 12q^{83} + 16q^{85} + 12q^{86} + 26q^{89} - 6q^{91} - 20q^{92} - 36q^{94} - 20q^{95} - 14q^{97} + q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7623))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 7 11
7623.2.a.a \(1\) \(60.870\) \(\Q\) None \(-2\) \(0\) \(-1\) \(1\) \(-\) \(-\) \(-\) \(q-2q^{2}+2q^{4}-q^{5}+q^{7}+2q^{10}+\cdots\)
7623.2.a.b \(1\) \(60.870\) \(\Q\) None \(-2\) \(0\) \(-1\) \(1\) \(+\) \(-\) \(-\) \(q-2q^{2}+2q^{4}-q^{5}+q^{7}+2q^{10}+\cdots\)
7623.2.a.c \(1\) \(60.870\) \(\Q\) None \(-2\) \(0\) \(1\) \(-1\) \(+\) \(+\) \(-\) \(q-2q^{2}+2q^{4}+q^{5}-q^{7}-2q^{10}+\cdots\)
7623.2.a.d \(1\) \(60.870\) \(\Q\) None \(-2\) \(0\) \(3\) \(-1\) \(-\) \(+\) \(-\) \(q-2q^{2}+2q^{4}+3q^{5}-q^{7}-6q^{10}+\cdots\)
7623.2.a.e \(1\) \(60.870\) \(\Q\) None \(-1\) \(0\) \(-1\) \(-1\) \(-\) \(+\) \(-\) \(q-q^{2}-q^{4}-q^{5}-q^{7}+3q^{8}+q^{10}+\cdots\)
7623.2.a.f \(1\) \(60.870\) \(\Q\) None \(-1\) \(0\) \(2\) \(-1\) \(-\) \(+\) \(-\) \(q-q^{2}-q^{4}+2q^{5}-q^{7}+3q^{8}-2q^{10}+\cdots\)
7623.2.a.g \(1\) \(60.870\) \(\Q\) None \(-1\) \(0\) \(2\) \(1\) \(-\) \(-\) \(-\) \(q-q^{2}-q^{4}+2q^{5}+q^{7}+3q^{8}-2q^{10}+\cdots\)
7623.2.a.h \(1\) \(60.870\) \(\Q\) None \(-1\) \(0\) \(3\) \(1\) \(-\) \(-\) \(-\) \(q-q^{2}-q^{4}+3q^{5}+q^{7}+3q^{8}-3q^{10}+\cdots\)
7623.2.a.i \(1\) \(60.870\) \(\Q\) None \(0\) \(0\) \(-3\) \(-1\) \(-\) \(+\) \(-\) \(q-2q^{4}-3q^{5}-q^{7}+4q^{13}+4q^{16}+\cdots\)
7623.2.a.j \(1\) \(60.870\) \(\Q\) None \(0\) \(0\) \(1\) \(1\) \(-\) \(-\) \(-\) \(q-2q^{4}+q^{5}+q^{7}+4q^{13}+4q^{16}+\cdots\)
7623.2.a.k \(1\) \(60.870\) \(\Q\) None \(0\) \(0\) \(3\) \(-1\) \(-\) \(+\) \(-\) \(q-2q^{4}+3q^{5}-q^{7}+4q^{13}+4q^{16}+\cdots\)
7623.2.a.l \(1\) \(60.870\) \(\Q\) None \(0\) \(0\) \(3\) \(1\) \(-\) \(-\) \(-\) \(q-2q^{4}+3q^{5}+q^{7}-4q^{13}+4q^{16}+\cdots\)
7623.2.a.m \(1\) \(60.870\) \(\Q\) None \(1\) \(0\) \(-1\) \(1\) \(-\) \(-\) \(-\) \(q+q^{2}-q^{4}-q^{5}+q^{7}-3q^{8}-q^{10}+\cdots\)
7623.2.a.n \(1\) \(60.870\) \(\Q\) None \(1\) \(0\) \(2\) \(1\) \(-\) \(-\) \(-\) \(q+q^{2}-q^{4}+2q^{5}+q^{7}-3q^{8}+2q^{10}+\cdots\)
7623.2.a.o \(1\) \(60.870\) \(\Q\) None \(1\) \(0\) \(3\) \(-1\) \(-\) \(+\) \(-\) \(q+q^{2}-q^{4}+3q^{5}-q^{7}-3q^{8}+3q^{10}+\cdots\)
7623.2.a.p \(1\) \(60.870\) \(\Q\) None \(2\) \(0\) \(-1\) \(-1\) \(+\) \(+\) \(-\) \(q+2q^{2}+2q^{4}-q^{5}-q^{7}-2q^{10}+\cdots\)
7623.2.a.q \(1\) \(60.870\) \(\Q\) None \(2\) \(0\) \(-1\) \(-1\) \(-\) \(+\) \(-\) \(q+2q^{2}+2q^{4}-q^{5}-q^{7}-2q^{10}+\cdots\)
7623.2.a.r \(1\) \(60.870\) \(\Q\) None \(2\) \(0\) \(1\) \(1\) \(+\) \(-\) \(-\) \(q+2q^{2}+2q^{4}+q^{5}+q^{7}+2q^{10}+\cdots\)
7623.2.a.s \(1\) \(60.870\) \(\Q\) None \(2\) \(0\) \(3\) \(1\) \(-\) \(-\) \(-\) \(q+2q^{2}+2q^{4}+3q^{5}+q^{7}+6q^{10}+\cdots\)
7623.2.a.t \(2\) \(60.870\) \(\Q(\sqrt{5}) \) None \(-3\) \(0\) \(-2\) \(-2\) \(-\) \(+\) \(-\) \(q+(-1-\beta )q^{2}+3\beta q^{4}-q^{5}-q^{7}+\cdots\)
7623.2.a.u \(2\) \(60.870\) \(\Q(\sqrt{5}) \) None \(-3\) \(0\) \(-1\) \(2\) \(-\) \(-\) \(+\) \(q+(-1-\beta )q^{2}+3\beta q^{4}-\beta q^{5}+q^{7}+\cdots\)
7623.2.a.v \(2\) \(60.870\) \(\Q(\sqrt{5}) \) None \(-3\) \(0\) \(2\) \(-2\) \(+\) \(+\) \(-\) \(q+(-1-\beta )q^{2}+3\beta q^{4}+q^{5}-q^{7}+\cdots\)
7623.2.a.w \(2\) \(60.870\) \(\Q(\sqrt{5}) \) None \(-2\) \(0\) \(-1\) \(-2\) \(-\) \(+\) \(-\) \(q-q^{2}-q^{4}+(-2+3\beta )q^{5}-q^{7}+3q^{8}+\cdots\)
7623.2.a.x \(2\) \(60.870\) \(\Q(\sqrt{3}) \) None \(-2\) \(0\) \(4\) \(-2\) \(-\) \(+\) \(-\) \(q+(-1+\beta )q^{2}+(2-2\beta )q^{4}+(2-\beta )q^{5}+\cdots\)
7623.2.a.y \(2\) \(60.870\) \(\Q(\sqrt{5}) \) None \(-1\) \(0\) \(0\) \(2\) \(-\) \(-\) \(+\) \(q-\beta q^{2}+(-1+\beta )q^{4}+(-1+2\beta )q^{5}+\cdots\)
7623.2.a.z \(2\) \(60.870\) \(\Q(\sqrt{5}) \) None \(-1\) \(0\) \(1\) \(2\) \(-\) \(-\) \(-\) \(q-\beta q^{2}+(-1+\beta )q^{4}+(1-\beta )q^{5}+q^{7}+\cdots\)
7623.2.a.ba \(2\) \(60.870\) \(\Q(\sqrt{5}) \) None \(-1\) \(0\) \(3\) \(2\) \(-\) \(-\) \(+\) \(q-\beta q^{2}+(-1+\beta )q^{4}+(1+\beta )q^{5}+q^{7}+\cdots\)
7623.2.a.bb \(2\) \(60.870\) \(\Q(\sqrt{5}) \) None \(-1\) \(0\) \(4\) \(-2\) \(-\) \(+\) \(+\) \(q-\beta q^{2}+(-1+\beta )q^{4}+(1+2\beta )q^{5}+\cdots\)
7623.2.a.bc \(2\) \(60.870\) \(\Q(\sqrt{13}) \) None \(-1\) \(0\) \(0\) \(-2\) \(-\) \(+\) \(-\) \(q-\beta q^{2}+(1+\beta )q^{4}+(1-2\beta )q^{5}-q^{7}+\cdots\)
7623.2.a.bd \(2\) \(60.870\) \(\Q(\sqrt{13}) \) None \(-1\) \(0\) \(2\) \(2\) \(+\) \(-\) \(-\) \(q-\beta q^{2}+(1+\beta )q^{4}+q^{5}+q^{7}-3q^{8}+\cdots\)
7623.2.a.be \(2\) \(60.870\) \(\Q(\sqrt{17}) \) None \(-1\) \(0\) \(-2\) \(2\) \(-\) \(-\) \(-\) \(q-\beta q^{2}+(2+\beta )q^{4}-q^{5}+q^{7}+(-4+\cdots)q^{8}+\cdots\)
7623.2.a.bf \(2\) \(60.870\) \(\Q(\sqrt{21}) \) None \(-1\) \(0\) \(-6\) \(-2\) \(-\) \(+\) \(-\) \(q-\beta q^{2}+(3+\beta )q^{4}-3q^{5}-q^{7}+(-5+\cdots)q^{8}+\cdots\)
7623.2.a.bg \(2\) \(60.870\) \(\Q(\sqrt{13}) \) None \(0\) \(0\) \(0\) \(-2\) \(+\) \(+\) \(-\) \(q-2q^{4}-\beta q^{5}-q^{7}+2q^{13}+4q^{16}+\cdots\)
7623.2.a.bh \(2\) \(60.870\) \(\Q(\sqrt{13}) \) None \(0\) \(0\) \(0\) \(2\) \(+\) \(-\) \(-\) \(q-2q^{4}-\beta q^{5}+q^{7}-2q^{13}+4q^{16}+\cdots\)
7623.2.a.bi \(2\) \(60.870\) \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(0\) \(-2\) \(+\) \(+\) \(-\) \(q+\beta q^{2}+q^{4}+2\beta q^{5}-q^{7}-\beta q^{8}+\cdots\)
7623.2.a.bj \(2\) \(60.870\) \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(-1\) \(-2\) \(-\) \(+\) \(-\) \(q+(1-2\beta )q^{2}+3q^{4}-\beta q^{5}-q^{7}+(1+\cdots)q^{8}+\cdots\)
7623.2.a.bk \(2\) \(60.870\) \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(-1\) \(2\) \(-\) \(-\) \(+\) \(q+(1-2\beta )q^{2}+3q^{4}+(-1+\beta )q^{5}+\cdots\)
7623.2.a.bl \(2\) \(60.870\) \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(4\) \(-2\) \(-\) \(+\) \(-\) \(q-\beta q^{2}+3q^{4}+2q^{5}-q^{7}-\beta q^{8}+\cdots\)
7623.2.a.bm \(2\) \(60.870\) \(\Q(\sqrt{5}) \) None \(1\) \(0\) \(-2\) \(-2\) \(-\) \(+\) \(-\) \(q+\beta q^{2}+(-1+\beta )q^{4}-q^{5}-q^{7}+(1+\cdots)q^{8}+\cdots\)
7623.2.a.bn \(2\) \(60.870\) \(\Q(\sqrt{5}) \) None \(1\) \(0\) \(0\) \(-2\) \(-\) \(+\) \(+\) \(q+\beta q^{2}+(-1+\beta )q^{4}+(-1+2\beta )q^{5}+\cdots\)
7623.2.a.bo \(2\) \(60.870\) \(\Q(\sqrt{5}) \) None \(1\) \(0\) \(1\) \(-2\) \(-\) \(+\) \(+\) \(q+\beta q^{2}+(-1+\beta )q^{4}+(1-\beta )q^{5}-q^{7}+\cdots\)
7623.2.a.bp \(2\) \(60.870\) \(\Q(\sqrt{5}) \) None \(1\) \(0\) \(3\) \(-2\) \(-\) \(+\) \(-\) \(q+\beta q^{2}+(-1+\beta )q^{4}+(1+\beta )q^{5}-q^{7}+\cdots\)
7623.2.a.bq \(2\) \(60.870\) \(\Q(\sqrt{5}) \) None \(1\) \(0\) \(4\) \(2\) \(-\) \(-\) \(+\) \(q+\beta q^{2}+(-1+\beta )q^{4}+(1+2\beta )q^{5}+\cdots\)
7623.2.a.br \(2\) \(60.870\) \(\Q(\sqrt{13}) \) None \(1\) \(0\) \(-2\) \(2\) \(+\) \(-\) \(-\) \(q+\beta q^{2}+(1+\beta )q^{4}-q^{5}+q^{7}+3q^{8}+\cdots\)
7623.2.a.bs \(2\) \(60.870\) \(\Q(\sqrt{13}) \) None \(1\) \(0\) \(0\) \(2\) \(-\) \(-\) \(-\) \(q+\beta q^{2}+(1+\beta )q^{4}+(1-2\beta )q^{5}+q^{7}+\cdots\)
7623.2.a.bt \(2\) \(60.870\) \(\Q(\sqrt{17}) \) None \(1\) \(0\) \(-2\) \(-2\) \(-\) \(+\) \(-\) \(q+\beta q^{2}+(2+\beta )q^{4}-q^{5}-q^{7}+(4+\beta )q^{8}+\cdots\)
7623.2.a.bu \(2\) \(60.870\) \(\Q(\sqrt{5}) \) None \(2\) \(0\) \(-1\) \(2\) \(-\) \(-\) \(+\) \(q+q^{2}-q^{4}+(-2+3\beta )q^{5}+q^{7}-3q^{8}+\cdots\)
7623.2.a.bv \(2\) \(60.870\) \(\Q(\sqrt{3}) \) None \(2\) \(0\) \(4\) \(2\) \(-\) \(-\) \(-\) \(q+(1+\beta )q^{2}+(2+2\beta )q^{4}+(2+\beta )q^{5}+\cdots\)
7623.2.a.bw \(2\) \(60.870\) \(\Q(\sqrt{5}) \) None \(3\) \(0\) \(-2\) \(-2\) \(+\) \(+\) \(-\) \(q+(1+\beta )q^{2}+3\beta q^{4}-q^{5}-q^{7}+(1+\cdots)q^{8}+\cdots\)
7623.2.a.bx \(2\) \(60.870\) \(\Q(\sqrt{5}) \) None \(3\) \(0\) \(-2\) \(2\) \(-\) \(-\) \(-\) \(q+(1+\beta )q^{2}+3\beta q^{4}-q^{5}+q^{7}+(1+\cdots)q^{8}+\cdots\)
7623.2.a.by \(2\) \(60.870\) \(\Q(\sqrt{5}) \) None \(3\) \(0\) \(-1\) \(-2\) \(-\) \(+\) \(-\) \(q+(1+\beta )q^{2}+3\beta q^{4}-\beta q^{5}-q^{7}+(1+\cdots)q^{8}+\cdots\)
7623.2.a.bz \(3\) \(60.870\) 3.3.568.1 None \(-2\) \(0\) \(-1\) \(3\) \(-\) \(-\) \(+\) \(q+(-1+\beta _{1})q^{2}+(3+\beta _{2})q^{4}+\beta _{2}q^{5}+\cdots\)
7623.2.a.ca \(3\) \(60.870\) 3.3.316.1 None \(-1\) \(0\) \(-1\) \(3\) \(-\) \(-\) \(-\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-\beta _{1}+\beta _{2})q^{5}+\cdots\)
7623.2.a.cb \(3\) \(60.870\) 3.3.837.1 None \(0\) \(0\) \(0\) \(3\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-\beta _{1}+\beta _{2})q^{5}+\cdots\)
7623.2.a.cc \(3\) \(60.870\) 3.3.316.1 None \(1\) \(0\) \(-1\) \(-3\) \(-\) \(+\) \(-\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-\beta _{1}+\beta _{2})q^{5}+\cdots\)
7623.2.a.cd \(3\) \(60.870\) 3.3.229.1 None \(2\) \(0\) \(-4\) \(3\) \(-\) \(-\) \(-\) \(q+(1+\beta _{2})q^{2}+(2+\beta _{1})q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
7623.2.a.ce \(3\) \(60.870\) 3.3.568.1 None \(2\) \(0\) \(-1\) \(-3\) \(-\) \(+\) \(+\) \(q+(1-\beta _{1})q^{2}+(3+\beta _{2})q^{4}+\beta _{2}q^{5}+\cdots\)
7623.2.a.cf \(4\) \(60.870\) 4.4.7488.1 None \(-2\) \(0\) \(-6\) \(4\) \(-\) \(-\) \(+\) \(q+\beta _{3}q^{2}+(1-\beta _{2})q^{4}+(-1+\beta _{3})q^{5}+\cdots\)
7623.2.a.cg \(4\) \(60.870\) 4.4.7488.1 None \(-2\) \(0\) \(2\) \(-4\) \(-\) \(+\) \(+\) \(q+\beta _{3}q^{2}+(1-\beta _{2})q^{4}+(1+\beta _{3})q^{5}+\cdots\)
7623.2.a.ch \(4\) \(60.870\) 4.4.2525.1 None \(-2\) \(0\) \(6\) \(-4\) \(-\) \(+\) \(+\) \(q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)
7623.2.a.ci \(4\) \(60.870\) 4.4.725.1 None \(-1\) \(0\) \(4\) \(-4\) \(-\) \(+\) \(+\) \(q+(-1+\beta _{1}+\beta _{2})q^{2}+(\beta _{1}+\beta _{3})q^{4}+\cdots\)
7623.2.a.cj \(4\) \(60.870\) \(\Q(\sqrt{2}, \sqrt{7})\) None \(0\) \(0\) \(0\) \(-4\) \(+\) \(+\) \(-\) \(q+\beta _{1}q^{2}-\beta _{3}q^{5}-q^{7}-2\beta _{1}q^{8}-\beta _{2}q^{10}+\cdots\)
7623.2.a.ck \(4\) \(60.870\) \(\Q(\sqrt{2}, \sqrt{7})\) None \(0\) \(0\) \(0\) \(4\) \(+\) \(-\) \(-\) \(q+\beta _{1}q^{2}-\beta _{3}q^{5}+q^{7}-2\beta _{1}q^{8}-\beta _{2}q^{10}+\cdots\)
7623.2.a.cl \(4\) \(60.870\) 4.4.725.1 None \(1\) \(0\) \(4\) \(4\) \(-\) \(-\) \(-\) \(q+(1-\beta _{1}-\beta _{2})q^{2}+(\beta _{1}+\beta _{3})q^{4}+2\beta _{2}q^{5}+\cdots\)
7623.2.a.cm \(4\) \(60.870\) 4.4.7488.1 None \(2\) \(0\) \(-6\) \(-4\) \(-\) \(+\) \(+\) \(q-\beta _{3}q^{2}+(1-\beta _{2})q^{4}+(-1+\beta _{3})q^{5}+\cdots\)
7623.2.a.cn \(4\) \(60.870\) 4.4.7488.1 None \(2\) \(0\) \(2\) \(4\) \(-\) \(-\) \(+\) \(q-\beta _{3}q^{2}+(1-\beta _{2})q^{4}+(1+\beta _{3})q^{5}+\cdots\)
7623.2.a.co \(4\) \(60.870\) 4.4.2525.1 None \(2\) \(0\) \(6\) \(4\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)
7623.2.a.cp \(6\) \(60.870\) 6.6.7674048.1 None \(-4\) \(0\) \(4\) \(6\) \(-\) \(-\) \(+\) \(q+(-1+\beta _{1})q^{2}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots\)
7623.2.a.cq \(6\) \(60.870\) 6.6.3829849.1 None \(0\) \(0\) \(0\) \(-6\) \(+\) \(+\) \(+\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots\)
7623.2.a.cr \(6\) \(60.870\) 6.6.3829849.1 None \(0\) \(0\) \(0\) \(6\) \(+\) \(-\) \(+\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(\beta _{1}-\beta _{3})q^{5}+\cdots\)
7623.2.a.cs \(6\) \(60.870\) 6.6.7674048.1 None \(4\) \(0\) \(4\) \(-6\) \(-\) \(+\) \(+\) \(q+(1-\beta _{1})q^{2}+(1-\beta _{1}+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots\)
7623.2.a.ct \(8\) \(60.870\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-1\) \(0\) \(-10\) \(8\) \(-\) \(-\) \(+\) \(q-\beta _{1}q^{2}+(1+\beta _{5}+\beta _{6})q^{4}+(-2-\beta _{2}+\cdots)q^{5}+\cdots\)
7623.2.a.cu \(8\) \(60.870\) 8.8.6988960000.1 None \(0\) \(0\) \(0\) \(-8\) \(+\) \(+\) \(+\) \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{1}+\beta _{7})q^{5}-q^{7}+\cdots\)
7623.2.a.cv \(8\) \(60.870\) 8.8.6988960000.1 None \(0\) \(0\) \(0\) \(8\) \(+\) \(-\) \(-\) \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-\beta _{1}-\beta _{7})q^{5}+\cdots\)
7623.2.a.cw \(8\) \(60.870\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(1\) \(0\) \(-10\) \(-8\) \(-\) \(+\) \(-\) \(q+\beta _{1}q^{2}+(1+\beta _{5}+\beta _{6})q^{4}+(-2-\beta _{2}+\cdots)q^{5}+\cdots\)
7623.2.a.cx \(10\) \(60.870\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(0\) \(-5\) \(-10\) \(-\) \(+\) \(+\) \(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+\beta _{6}q^{5}-q^{7}+\cdots\)
7623.2.a.cy \(10\) \(60.870\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(0\) \(-5\) \(10\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+\beta _{6}q^{5}+q^{7}+\cdots\)
7623.2.a.cz \(12\) \(60.870\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(-12\) \(+\) \(+\) \(+\) \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+\beta _{8}q^{5}-q^{7}+\cdots\)
7623.2.a.da \(12\) \(60.870\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(12\) \(+\) \(-\) \(+\) \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}-\beta _{8}q^{5}+q^{7}+\cdots\)
7623.2.a.db \(16\) \(60.870\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(-16\) \(+\) \(+\) \(-\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{7}q^{5}-q^{7}+\cdots\)
7623.2.a.dc \(16\) \(60.870\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(16\) \(+\) \(-\) \(+\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{7}q^{5}+q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7623))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(7623)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(231))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(363))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(693))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(847))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1089))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2541))\)\(^{\oplus 2}\)