Properties

Label 315.2.cc
Level 315
Weight 2
Character orbit cc
Rep. character \(\chi_{315}(92,\cdot)\)
Character field \(\Q(\zeta_{12})\)
Dimension 144
Newform subspaces 1
Sturm bound 96
Trace bound 0

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Defining parameters

Level: \( N \) = \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 315.cc (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 45 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 1 \)
Sturm bound: \(96\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(315, [\chi])\).

Total New Old
Modular forms 208 144 64
Cusp forms 176 144 32
Eisenstein series 32 0 32

Trace form

\( 144q + 4q^{3} + O(q^{10}) \) \( 144q + 4q^{3} - 12q^{11} - 16q^{12} + 16q^{15} + 72q^{16} - 64q^{18} - 48q^{20} - 4q^{21} - 24q^{23} - 12q^{25} - 32q^{27} - 20q^{30} - 60q^{32} - 16q^{33} - 16q^{36} - 24q^{37} + 72q^{38} + 48q^{41} - 40q^{42} + 40q^{45} - 48q^{46} + 12q^{47} + 104q^{48} - 76q^{51} - 24q^{55} - 4q^{57} - 92q^{60} + 8q^{63} - 72q^{65} - 80q^{66} - 12q^{67} - 64q^{72} - 108q^{75} - 24q^{76} + 72q^{78} + 32q^{81} - 96q^{82} + 120q^{83} - 48q^{85} - 144q^{86} + 116q^{87} - 48q^{88} + 252q^{90} + 24q^{91} + 156q^{92} - 44q^{93} + 120q^{95} - 96q^{96} - 60q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(315, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
315.2.cc.a \(144\) \(2.515\) None \(0\) \(4\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(315, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(315, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database