Properties

Label 315.2.cb
Level 315
Weight 2
Character orbit cb
Rep. character \(\chi_{315}(13,\cdot)\)
Character field \(\Q(\zeta_{12})\)
Dimension 176
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.cb (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 315 \)
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 208 208 0
Cusp forms 176 176 0
Eisenstein series 32 32 0

Trace form

\( 176q - 4q^{2} - 2q^{7} - 32q^{8} + O(q^{10}) \) \( 176q - 4q^{2} - 2q^{7} - 32q^{8} - 12q^{11} - 20q^{15} + 56q^{16} - 8q^{18} + 12q^{22} - 12q^{23} - 4q^{25} - 32q^{28} - 56q^{30} + 48q^{32} - 8q^{35} - 80q^{36} - 16q^{37} + 38q^{42} - 4q^{43} - 80q^{46} - 76q^{50} - 28q^{51} + 64q^{53} - 52q^{56} - 112q^{57} - 44q^{58} - 40q^{60} + 24q^{63} + 20q^{65} - 4q^{67} + 18q^{70} - 64q^{71} - 20q^{72} + 26q^{77} + 76q^{78} - 64q^{81} - 4q^{85} + 80q^{86} - 60q^{88} - 16q^{91} - 68q^{92} + 88q^{93} + 40q^{95} - 120q^{98} + O(q^{100}) \)

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.cb.a \(176\) \(2.515\) None \(-4\) \(0\) \(0\) \(-2\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database