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Properties

Label 315.10.d
Level $315$
Weight $10$
Character orbit 315.d
Rep. character $\chi_{315}(64,\cdot)$
Character field $\Q$
Dimension $134$
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.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 440 134 306
Cusp forms 424 134 290
Eisenstein series 16 0 16

Trace form

\( 134 q - 34476 q^{4} + 1470 q^{5} + O(q^{10}) \) \( 134 q - 34476 q^{4} + 1470 q^{5} + 6472 q^{10} + 132540 q^{11} - 153664 q^{14} + 10587596 q^{16} - 1380456 q^{19} - 2867080 q^{20} + 8658890 q^{25} + 2413124 q^{26} - 7743544 q^{29} + 242424 q^{31} - 25026172 q^{34} - 3102092 q^{35} + 78114644 q^{40} + 60920844 q^{41} - 158503264 q^{44} - 100255568 q^{46} - 772483334 q^{49} - 198260556 q^{50} + 28643744 q^{55} + 74479020 q^{56} - 586643040 q^{59} - 443019628 q^{61} - 3040631340 q^{64} + 120220328 q^{65} - 80126172 q^{70} + 272448344 q^{71} + 162830520 q^{74} + 2046222848 q^{76} + 283274356 q^{79} + 1870645800 q^{80} - 1368964788 q^{85} - 51830696 q^{86} + 831757084 q^{89} - 978273044 q^{91} + 2698851508 q^{94} + 4090420484 q^{95} + O(q^{100}) \)

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

\( S_{10}^{\mathrm{old}}(315, [\chi]) \simeq \) \(S_{10}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)