Properties

Label 315.2.u
Level 315
Weight 2
Character orbit u
Rep. character \(\chi_{315}(59,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 88
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.u (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 315 \)
Character field: \(\Q(\zeta_{6})\)
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 104 104 0
Cusp forms 88 88 0
Eisenstein series 16 16 0

Trace form

\( 88q - 38q^{4} - 6q^{5} + 12q^{6} - 6q^{9} + O(q^{10}) \) \( 88q - 38q^{4} - 6q^{5} + 12q^{6} - 6q^{9} - 6q^{10} - 12q^{14} - 6q^{15} - 26q^{16} - 12q^{19} + 6q^{20} - 12q^{21} - 42q^{24} - 2q^{25} + 12q^{26} + 6q^{29} - 18q^{30} - 6q^{31} + 12q^{34} - 36q^{36} - 6q^{41} + 84q^{44} - 12q^{45} - 18q^{46} + 10q^{49} + 30q^{50} - 6q^{51} - 48q^{54} - 90q^{56} - 6q^{59} + 54q^{60} + 12q^{61} - 8q^{64} + 54q^{65} + 78q^{66} - 60q^{69} - 30q^{70} + 12q^{75} + 48q^{76} + 8q^{79} + 69q^{80} + 42q^{81} + 120q^{84} - 7q^{85} - 72q^{89} - 33q^{90} + 20q^{91} - 6q^{94} - 93q^{95} - 12q^{96} + 30q^{99} + O(q^{100}) \)

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.u.a \(88\) \(2.515\) None \(0\) \(0\) \(-6\) \(0\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database