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Properties

Label 1575.2.s
Level $1575$
Weight $2$
Character orbit 1575.s
Rep. character $\chi_{1575}(499,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $280$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1575.s (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 315 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1575, [\chi])\).

Total New Old
Modular forms 504 296 208
Cusp forms 456 280 176
Eisenstein series 48 16 32

Trace form

\( 280 q - 268 q^{4} - 20 q^{6} + 14 q^{9} + O(q^{10}) \) \( 280 q - 268 q^{4} - 20 q^{6} + 14 q^{9} + 6 q^{11} + 14 q^{14} + 244 q^{16} + 4 q^{19} - 8 q^{21} + 56 q^{24} + 24 q^{26} + 24 q^{29} - 4 q^{31} - 40 q^{36} + 54 q^{39} + 24 q^{41} - 24 q^{46} - 10 q^{49} + 62 q^{51} - 38 q^{54} - 96 q^{56} + 100 q^{59} + 20 q^{61} - 184 q^{64} - 24 q^{66} + 60 q^{69} - 60 q^{71} - 50 q^{74} - 4 q^{76} + 4 q^{79} - 54 q^{81} - 4 q^{84} - 54 q^{86} - 26 q^{89} + 20 q^{91} + 84 q^{94} - 190 q^{96} + 50 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1575, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1575, [\chi])\) into lower level spaces

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