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Properties

Label 1575.4.v
Level $1575$
Weight $4$
Character orbit 1575.v
Rep. character $\chi_{1575}(299,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $856$
Sturm bound $960$

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Defining parameters

Level: \( N \) \(=\) \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1575.v (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 315 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1575, [\chi])\).

Total New Old
Modular forms 1464 872 592
Cusp forms 1416 856 560
Eisenstein series 48 16 32

Trace form

\( 856 q - 1698 q^{4} - 48 q^{6} - 2 q^{9} + O(q^{10}) \) \( 856 q - 1698 q^{4} - 48 q^{6} - 2 q^{9} + 270 q^{14} - 6670 q^{16} + 12 q^{19} + 708 q^{21} - 444 q^{24} - 48 q^{26} - 240 q^{29} - 6 q^{31} + 48 q^{34} - 1524 q^{36} + 1026 q^{39} + 1236 q^{41} - 336 q^{44} - 476 q^{46} + 794 q^{49} - 1218 q^{51} - 4446 q^{54} - 1896 q^{56} + 6 q^{59} - 114 q^{61} + 51440 q^{64} - 342 q^{66} - 2010 q^{69} + 288 q^{76} - 1190 q^{79} - 1654 q^{81} - 8382 q^{84} - 372 q^{89} - 1380 q^{91} + 6 q^{94} + 5754 q^{96} + 7478 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1575, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1575, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1575, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)