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Properties

Label 1575.4.s
Level $1575$
Weight $4$
Character orbit 1575.s
Rep. character $\chi_{1575}(499,\cdot)$
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.s (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

\( 856 q - 3388 q^{4} - 8 q^{6} + 26 q^{9} + O(q^{10}) \) \( 856 q - 3388 q^{4} - 8 q^{6} + 26 q^{9} - 6 q^{11} - 22 q^{14} + 13276 q^{16} + 4 q^{19} + 106 q^{21} + 56 q^{24} - 612 q^{26} + 504 q^{29} - 4 q^{31} - 12 q^{34} - 532 q^{36} + 852 q^{39} - 1728 q^{41} + 372 q^{44} + 468 q^{46} + 398 q^{49} + 1226 q^{51} - 770 q^{54} + 2472 q^{56} - 5660 q^{59} + 68 q^{61} - 50896 q^{64} + 2784 q^{66} + 3990 q^{69} - 4200 q^{71} - 362 q^{74} + 92 q^{76} - 2372 q^{79} + 4830 q^{81} - 1864 q^{84} + 1866 q^{86} + 1432 q^{89} + 1364 q^{91} + 5028 q^{94} + 5018 q^{96} - 70 q^{99} + O(q^{100}) \)

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

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