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Properties

Label 315.4.bf
Level $315$
Weight $4$
Character orbit 315.bf
Rep. character $\chi_{315}(109,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $116$
Sturm bound $192$

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Defining parameters

Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 315.bf (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(192\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(315, [\chi])\).

Total New Old
Modular forms 304 124 180
Cusp forms 272 116 156
Eisenstein series 32 8 24

Trace form

\( 116 q + 222 q^{4} + 5 q^{5} + O(q^{10}) \) \( 116 q + 222 q^{4} + 5 q^{5} - 8 q^{10} + 48 q^{11} - 110 q^{14} - 790 q^{16} - 48 q^{19} + 368 q^{20} + 137 q^{25} - 218 q^{26} + 28 q^{29} - 6 q^{31} + 416 q^{34} + 403 q^{35} - 106 q^{40} + 592 q^{41} - 126 q^{44} + 430 q^{46} - 14 q^{49} - 2332 q^{50} + 1202 q^{55} - 2736 q^{56} + 322 q^{59} + 1568 q^{61} - 6012 q^{64} + 286 q^{65} - 1542 q^{70} + 3104 q^{71} + 1462 q^{74} - 388 q^{76} + 1894 q^{79} + 3640 q^{80} + 3558 q^{85} + 2120 q^{86} + 2604 q^{89} + 1684 q^{91} - 3146 q^{94} - 3597 q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(315, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(315, [\chi])\) into lower level spaces

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