↑

Properties

Label 1575.4.bg
Level $1575$
Weight $4$
Character orbit 1575.bg
Rep. character $\chi_{1575}(424,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $356$
Sturm bound $960$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1575.bg (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
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 1488 364 1124
Cusp forms 1392 356 1036
Eisenstein series 96 8 88

Trace form

\( 356 q + 706 q^{4} + O(q^{10}) \) \( 356 q + 706 q^{4} - 62 q^{11} + 338 q^{14} - 2826 q^{16} + 122 q^{19} + 114 q^{26} - 16 q^{29} - 258 q^{31} - 104 q^{34} + 344 q^{41} + 792 q^{44} - 1156 q^{46} + 84 q^{49} + 3774 q^{56} + 446 q^{59} - 1002 q^{61} - 19000 q^{64} - 5072 q^{71} - 2742 q^{74} + 4820 q^{76} - 854 q^{79} + 1188 q^{86} - 1710 q^{89} - 5188 q^{91} + 4786 q^{94} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1575, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)