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Properties

Label 315.10.bf
Level $315$
Weight $10$
Character orbit 315.bf
Rep. character $\chi_{315}(109,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $356$
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.bf (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 880 364 516
Cusp forms 848 356 492
Eisenstein series 32 8 24

Trace form

\( 356 q + 45054 q^{4} + 285 q^{5} + O(q^{10}) \) \( 356 q + 45054 q^{4} + 285 q^{5} + 15700 q^{10} + 51408 q^{11} + 502462 q^{14} - 11002566 q^{16} + 1081088 q^{19} - 662336 q^{20} + 3480701 q^{25} + 10213594 q^{26} + 10674676 q^{29} - 12099478 q^{31} + 11333024 q^{34} - 4603189 q^{35} + 33143438 q^{40} - 62636976 q^{41} - 103230182 q^{44} + 101875494 q^{46} - 157542714 q^{49} + 455089284 q^{50} + 127740898 q^{55} + 94310784 q^{56} - 394583406 q^{59} - 143715852 q^{61} - 5432943260 q^{64} + 339019282 q^{65} + 31554150 q^{70} - 835013312 q^{71} + 497689842 q^{74} + 153484300 q^{76} - 440796746 q^{79} + 361564056 q^{80} - 2722868530 q^{85} + 537431948 q^{86} - 1162710640 q^{89} - 210659788 q^{91} - 64378086 q^{94} - 602198285 q^{95} + O(q^{100}) \)

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

\( S_{10}^{\mathrm{old}}(315, [\chi]) \simeq \) \(S_{10}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)