Properties

Label 315.2.bx
Level 315
Weight 2
Character orbit bx
Rep. character \(\chi_{315}(2,\cdot)\)
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.bx (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

\( 176q - 6q^{2} - 2q^{3} - 24q^{6} - 2q^{7} + O(q^{10}) \) \( 176q - 6q^{2} - 2q^{3} - 24q^{6} - 2q^{7} - 4q^{10} - 22q^{12} - 4q^{13} - 14q^{15} + 68q^{16} - 18q^{17} - 10q^{18} - 12q^{20} + 20q^{21} + 4q^{22} - 4q^{25} - 32q^{27} - 4q^{28} - 20q^{30} + 4q^{31} - 90q^{32} + 32q^{33} + 8q^{36} - 4q^{37} - 36q^{40} - 36q^{41} + 14q^{42} - 4q^{43} - 68q^{45} + 4q^{46} - 6q^{47} + 38q^{48} + 36q^{50} + 20q^{51} - 52q^{52} + 4q^{55} - 96q^{56} + 32q^{57} - 12q^{58} - 74q^{60} - 8q^{61} + 14q^{63} - 78q^{65} - 92q^{66} + 2q^{67} - 42q^{70} - 46q^{72} - 4q^{73} + 54q^{75} - 24q^{76} + 42q^{77} + 54q^{78} + 36q^{80} + 20q^{81} - 8q^{82} - 12q^{83} - 4q^{85} - 28q^{87} + 12q^{88} - 24q^{90} - 16q^{91} + 72q^{92} + 4q^{93} - 66q^{95} - 4q^{97} + 12q^{98} + O(q^{100}) \)

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.bx.a \(176\) \(2.515\) None \(-6\) \(-2\) \(0\) \(-2\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database