Properties

Label 7406.2.a
Level $7406$
Weight $2$
Character orbit 7406.a
Rep. character $\chi_{7406}(1,\cdot)$
Character field $\Q$
Dimension $252$
Newform subspaces $48$
Sturm bound $2208$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 7406 = 2 \cdot 7 \cdot 23^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7406.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 48 \)
Sturm bound: \(2208\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\), \(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7406))\).

Total New Old
Modular forms 1152 252 900
Cusp forms 1057 252 805
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.

\(2\)\(7\)\(23\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(28\)
\(+\)\(+\)\(-\)\(-\)\(36\)
\(+\)\(-\)\(+\)\(-\)\(38\)
\(+\)\(-\)\(-\)\(+\)\(25\)
\(-\)\(+\)\(+\)\(-\)\(32\)
\(-\)\(+\)\(-\)\(+\)\(30\)
\(-\)\(-\)\(+\)\(+\)\(22\)
\(-\)\(-\)\(-\)\(-\)\(41\)
Plus space\(+\)\(105\)
Minus space\(-\)\(147\)

Trace form

\( 252q - 2q^{2} + 2q^{3} + 252q^{4} + 2q^{5} - 2q^{6} - 2q^{8} + 248q^{9} + O(q^{10}) \) \( 252q - 2q^{2} + 2q^{3} + 252q^{4} + 2q^{5} - 2q^{6} - 2q^{8} + 248q^{9} - 6q^{10} + 2q^{12} + 6q^{13} + 2q^{14} + 16q^{15} + 252q^{16} + 4q^{17} - 6q^{18} + 6q^{19} + 2q^{20} - 2q^{21} - 2q^{24} + 272q^{25} - 2q^{26} + 20q^{27} + 4q^{29} + 20q^{31} - 2q^{32} - 8q^{34} + 2q^{35} + 248q^{36} + 8q^{37} - 6q^{38} + 32q^{39} - 6q^{40} + 12q^{41} + 2q^{42} - 6q^{45} + 12q^{47} + 2q^{48} + 252q^{49} - 2q^{50} - 20q^{51} + 6q^{52} + 12q^{53} - 20q^{54} + 16q^{55} + 2q^{56} + 4q^{57} + 8q^{58} + 6q^{59} + 16q^{60} - 22q^{61} + 20q^{62} + 12q^{63} + 252q^{64} - 36q^{65} + 16q^{66} + 4q^{67} + 4q^{68} + 2q^{70} + 32q^{71} - 6q^{72} + 8q^{73} + 12q^{74} + 14q^{75} + 6q^{76} - 12q^{77} + 16q^{78} + 24q^{79} + 2q^{80} + 272q^{81} - 16q^{82} - 10q^{83} - 2q^{84} - 44q^{85} - 16q^{86} - 36q^{87} + 34q^{90} - 6q^{91} - 32q^{93} - 20q^{94} + 16q^{95} - 2q^{96} + 4q^{97} - 2q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7406))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 7 23
7406.2.a.a \(1\) \(59.137\) \(\Q\) None \(-1\) \(-2\) \(0\) \(-1\) \(+\) \(+\) \(-\) \(q-q^{2}-2q^{3}+q^{4}+2q^{6}-q^{7}-q^{8}+\cdots\)
7406.2.a.b \(1\) \(59.137\) \(\Q\) None \(-1\) \(0\) \(0\) \(-1\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}-q^{7}-q^{8}-3q^{9}+4q^{11}+\cdots\)
7406.2.a.c \(1\) \(59.137\) \(\Q\) None \(-1\) \(0\) \(0\) \(1\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{7}-q^{8}-3q^{9}-4q^{11}+\cdots\)
7406.2.a.d \(1\) \(59.137\) \(\Q\) None \(-1\) \(0\) \(2\) \(-1\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}+2q^{5}-q^{7}-q^{8}-3q^{9}+\cdots\)
7406.2.a.e \(1\) \(59.137\) \(\Q\) None \(-1\) \(2\) \(0\) \(-1\) \(+\) \(+\) \(-\) \(q-q^{2}+2q^{3}+q^{4}-2q^{6}-q^{7}-q^{8}+\cdots\)
7406.2.a.f \(1\) \(59.137\) \(\Q\) None \(1\) \(-2\) \(2\) \(1\) \(-\) \(-\) \(-\) \(q+q^{2}-2q^{3}+q^{4}+2q^{5}-2q^{6}+q^{7}+\cdots\)
7406.2.a.g \(1\) \(59.137\) \(\Q\) None \(1\) \(-1\) \(-4\) \(-1\) \(-\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}-4q^{5}-q^{6}-q^{7}+\cdots\)
7406.2.a.h \(1\) \(59.137\) \(\Q\) None \(1\) \(-1\) \(4\) \(1\) \(-\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}+4q^{5}-q^{6}+q^{7}+\cdots\)
7406.2.a.i \(1\) \(59.137\) \(\Q\) None \(1\) \(2\) \(2\) \(-1\) \(-\) \(+\) \(-\) \(q+q^{2}+2q^{3}+q^{4}+2q^{5}+2q^{6}-q^{7}+\cdots\)
7406.2.a.j \(2\) \(59.137\) \(\Q(\sqrt{5}) \) None \(-2\) \(-2\) \(2\) \(2\) \(+\) \(-\) \(-\) \(q-q^{2}+(-1-\beta )q^{3}+q^{4}+(1-\beta )q^{5}+\cdots\)
7406.2.a.k \(2\) \(59.137\) \(\Q(\sqrt{13}) \) None \(-2\) \(-1\) \(-1\) \(-2\) \(+\) \(+\) \(-\) \(q-q^{2}-\beta q^{3}+q^{4}+(-1+\beta )q^{5}+\beta q^{6}+\cdots\)
7406.2.a.l \(2\) \(59.137\) \(\Q(\sqrt{13}) \) None \(-2\) \(-1\) \(1\) \(2\) \(+\) \(-\) \(-\) \(q-q^{2}-\beta q^{3}+q^{4}+(1-\beta )q^{5}+\beta q^{6}+\cdots\)
7406.2.a.m \(2\) \(59.137\) \(\Q(\sqrt{6}) \) None \(-2\) \(0\) \(0\) \(-2\) \(+\) \(+\) \(-\) \(q-q^{2}+\beta q^{3}+q^{4}+\beta q^{5}-\beta q^{6}-q^{7}+\cdots\)
7406.2.a.n \(2\) \(59.137\) \(\Q(\sqrt{6}) \) None \(-2\) \(0\) \(0\) \(2\) \(+\) \(-\) \(-\) \(q-q^{2}+\beta q^{3}+q^{4}-\beta q^{5}-\beta q^{6}+q^{7}+\cdots\)
7406.2.a.o \(2\) \(59.137\) \(\Q(\sqrt{5}) \) None \(-2\) \(1\) \(-1\) \(2\) \(+\) \(-\) \(-\) \(q-q^{2}+\beta q^{3}+q^{4}+(-1+\beta )q^{5}-\beta q^{6}+\cdots\)
7406.2.a.p \(2\) \(59.137\) \(\Q(\sqrt{5}) \) None \(-2\) \(1\) \(1\) \(-2\) \(+\) \(+\) \(-\) \(q-q^{2}+\beta q^{3}+q^{4}+(1-\beta )q^{5}-\beta q^{6}+\cdots\)
7406.2.a.q \(2\) \(59.137\) \(\Q(\sqrt{2}) \) None \(-2\) \(4\) \(0\) \(-2\) \(+\) \(+\) \(+\) \(q-q^{2}+2q^{3}+q^{4}-2\beta q^{5}-2q^{6}+\cdots\)
7406.2.a.r \(2\) \(59.137\) \(\Q(\sqrt{2}) \) None \(-2\) \(4\) \(0\) \(2\) \(+\) \(-\) \(+\) \(q-q^{2}+2q^{3}+q^{4}-2\beta q^{5}-2q^{6}+\cdots\)
7406.2.a.s \(2\) \(59.137\) \(\Q(\sqrt{3}) \) None \(2\) \(-2\) \(-2\) \(-2\) \(-\) \(+\) \(-\) \(q+q^{2}+(-1+\beta )q^{3}+q^{4}+(-1-\beta )q^{5}+\cdots\)
7406.2.a.t \(3\) \(59.137\) 3.3.148.1 None \(3\) \(-2\) \(-2\) \(-3\) \(-\) \(+\) \(-\) \(q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(-1+\beta _{2})q^{5}+\cdots\)
7406.2.a.u \(3\) \(59.137\) 3.3.148.1 None \(3\) \(-2\) \(2\) \(3\) \(-\) \(-\) \(-\) \(q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(1-\beta _{2})q^{5}+\cdots\)
7406.2.a.v \(3\) \(59.137\) 3.3.1509.1 None \(3\) \(-1\) \(-4\) \(3\) \(-\) \(-\) \(-\) \(q+q^{2}-\beta _{1}q^{3}+q^{4}+(-1-\beta _{1})q^{5}+\cdots\)
7406.2.a.w \(3\) \(59.137\) 3.3.1509.1 None \(3\) \(-1\) \(4\) \(-3\) \(-\) \(+\) \(-\) \(q+q^{2}-\beta _{1}q^{3}+q^{4}+(1+\beta _{1})q^{5}-\beta _{1}q^{6}+\cdots\)
7406.2.a.x \(3\) \(59.137\) 3.3.316.1 None \(3\) \(2\) \(-4\) \(3\) \(-\) \(-\) \(-\) \(q+q^{2}+(1+\beta _{2})q^{3}+q^{4}+(-1+\beta _{2})q^{5}+\cdots\)
7406.2.a.y \(4\) \(59.137\) \(\Q(\zeta_{24})^+\) None \(-4\) \(-4\) \(0\) \(-4\) \(+\) \(+\) \(+\) \(q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
7406.2.a.z \(4\) \(59.137\) \(\Q(\zeta_{24})^+\) None \(-4\) \(-4\) \(0\) \(4\) \(+\) \(-\) \(+\) \(q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
7406.2.a.ba \(4\) \(59.137\) 4.4.449797.1 None \(4\) \(0\) \(-4\) \(-4\) \(-\) \(+\) \(-\) \(q+q^{2}+\beta _{1}q^{3}+q^{4}+(-1-\beta _{1})q^{5}+\cdots\)
7406.2.a.bb \(4\) \(59.137\) 4.4.4352.1 None \(4\) \(0\) \(-4\) \(4\) \(-\) \(-\) \(+\) \(q+q^{2}+(-\beta _{1}+\beta _{3})q^{3}+q^{4}+(-1+\cdots)q^{5}+\cdots\)
7406.2.a.bc \(4\) \(59.137\) 4.4.4352.1 None \(4\) \(0\) \(4\) \(-4\) \(-\) \(+\) \(+\) \(q+q^{2}+(-\beta _{1}+\beta _{3})q^{3}+q^{4}+(1-\beta _{2}+\cdots)q^{5}+\cdots\)
7406.2.a.bd \(4\) \(59.137\) 4.4.449797.1 None \(4\) \(0\) \(4\) \(4\) \(-\) \(-\) \(-\) \(q+q^{2}+\beta _{1}q^{3}+q^{4}+(1+\beta _{1})q^{5}+\beta _{1}q^{6}+\cdots\)
7406.2.a.be \(5\) \(59.137\) \(\Q(\zeta_{22})^+\) None \(-5\) \(-3\) \(-4\) \(5\) \(+\) \(-\) \(-\) \(q-q^{2}+(-1+\beta _{1}-\beta _{4})q^{3}+q^{4}+(-2+\cdots)q^{5}+\cdots\)
7406.2.a.bf \(5\) \(59.137\) \(\Q(\zeta_{22})^+\) None \(-5\) \(-3\) \(4\) \(-5\) \(+\) \(+\) \(+\) \(q-q^{2}+(-1+\beta _{1}-\beta _{4})q^{3}+q^{4}+(2+\cdots)q^{5}+\cdots\)
7406.2.a.bg \(5\) \(59.137\) \(\Q(\zeta_{22})^+\) None \(-5\) \(4\) \(-3\) \(-5\) \(+\) \(+\) \(+\) \(q-q^{2}+(1-\beta _{1})q^{3}+q^{4}+(-\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\)
7406.2.a.bh \(5\) \(59.137\) \(\Q(\zeta_{22})^+\) None \(-5\) \(4\) \(3\) \(5\) \(+\) \(-\) \(-\) \(q-q^{2}+(1-\beta _{1})q^{3}+q^{4}+(\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots\)
7406.2.a.bi \(6\) \(59.137\) 6.6.596217024.1 None \(-6\) \(0\) \(0\) \(-6\) \(+\) \(+\) \(-\) \(q-q^{2}+\beta _{1}q^{3}+q^{4}+(\beta _{1}-\beta _{3})q^{5}+\cdots\)
7406.2.a.bj \(6\) \(59.137\) 6.6.596217024.1 None \(-6\) \(0\) \(0\) \(6\) \(+\) \(-\) \(-\) \(q-q^{2}+\beta _{1}q^{3}+q^{4}+(-\beta _{1}+\beta _{3})q^{5}+\cdots\)
7406.2.a.bk \(6\) \(59.137\) 6.6.84770496.1 None \(6\) \(2\) \(-4\) \(-6\) \(-\) \(+\) \(-\) \(q+q^{2}+\beta _{1}q^{3}+q^{4}+(-1-\beta _{4})q^{5}+\cdots\)
7406.2.a.bl \(6\) \(59.137\) 6.6.84770496.1 None \(6\) \(2\) \(4\) \(6\) \(-\) \(-\) \(-\) \(q+q^{2}+\beta _{1}q^{3}+q^{4}+(1+\beta _{4})q^{5}+\beta _{1}q^{6}+\cdots\)
7406.2.a.bm \(8\) \(59.137\) 8.8.6120603648.1 None \(8\) \(0\) \(-8\) \(8\) \(-\) \(-\) \(+\) \(q+q^{2}-\beta _{1}q^{3}+q^{4}+(-1+\beta _{2}-\beta _{4}+\cdots)q^{5}+\cdots\)
7406.2.a.bn \(8\) \(59.137\) 8.8.6120603648.1 None \(8\) \(0\) \(8\) \(-8\) \(-\) \(+\) \(+\) \(q+q^{2}-\beta _{1}q^{3}+q^{4}+(1-\beta _{2}+\beta _{4}+\cdots)q^{5}+\cdots\)
7406.2.a.bo \(10\) \(59.137\) 10.10.\(\cdots\).1 None \(10\) \(-9\) \(-3\) \(-10\) \(-\) \(+\) \(-\) \(q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(\beta _{1}-\beta _{9})q^{5}+\cdots\)
7406.2.a.bp \(10\) \(59.137\) 10.10.\(\cdots\).1 None \(10\) \(-9\) \(3\) \(10\) \(-\) \(-\) \(+\) \(q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
7406.2.a.bq \(12\) \(59.137\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-12\) \(0\) \(0\) \(-12\) \(+\) \(+\) \(+\) \(q-q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{8}q^{5}-\beta _{1}q^{6}+\cdots\)
7406.2.a.br \(12\) \(59.137\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-12\) \(0\) \(0\) \(12\) \(+\) \(-\) \(+\) \(q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{8}q^{5}-\beta _{1}q^{6}+\cdots\)
7406.2.a.bs \(20\) \(59.137\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-20\) \(1\) \(-1\) \(-20\) \(+\) \(+\) \(-\) \(q-q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{12}q^{5}-\beta _{1}q^{6}+\cdots\)
7406.2.a.bt \(20\) \(59.137\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-20\) \(1\) \(1\) \(20\) \(+\) \(-\) \(+\) \(q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{12}q^{5}-\beta _{1}q^{6}+\cdots\)
7406.2.a.bu \(20\) \(59.137\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(20\) \(11\) \(-1\) \(-20\) \(-\) \(+\) \(+\) \(q+q^{2}+(1-\beta _{1})q^{3}+q^{4}-\beta _{12}q^{5}+\cdots\)
7406.2.a.bv \(20\) \(59.137\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(20\) \(11\) \(1\) \(20\) \(-\) \(-\) \(-\) \(q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+\beta _{12}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7406))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(7406)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(161))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(322))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(529))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1058))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3703))\)\(^{\oplus 2}\)