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Properties

Label 315.10.m
Level $315$
Weight $10$
Character orbit 315.m
Rep. character $\chi_{315}(8,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $216$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 315.m (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(315, [\chi])\).

Total New Old
Modular forms 880 216 664
Cusp forms 848 216 632
Eisenstein series 32 0 32

Trace form

\( 216 q + O(q^{10}) \) \( 216 q + 45792 q^{10} + 5832 q^{13} - 14891760 q^{16} - 4396896 q^{22} + 5770224 q^{25} + 27014400 q^{31} - 35345592 q^{37} + 228390624 q^{40} - 305209440 q^{43} + 31696128 q^{46} - 386971488 q^{52} + 712366848 q^{55} - 341266896 q^{58} - 360484416 q^{61} + 651734784 q^{67} - 614041344 q^{70} - 730358280 q^{73} - 3375863712 q^{76} + 85223520 q^{82} - 3127946400 q^{85} - 1464562800 q^{88} + 4322362104 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(315, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{10}^{\mathrm{old}}(315, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(315, [\chi]) \simeq \) \(S_{10}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)