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Properties

Label 1575.4.bm
Level $1575$
Weight $4$
Character orbit 1575.bm
Rep. character $\chi_{1575}(776,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $900$
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.bm (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
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 924 540
Cusp forms 1416 900 516
Eisenstein series 48 24 24

Trace form

\( 900 q + 6 q^{2} + 1778 q^{4} + 7 q^{7} + O(q^{10}) \) \( 900 q + 6 q^{2} + 1778 q^{4} + 7 q^{7} - 6 q^{11} - 54 q^{14} - 6934 q^{16} - 154 q^{18} + 9 q^{21} + 34 q^{22} - 402 q^{23} + 84 q^{28} - 246 q^{29} - 1068 q^{32} - 486 q^{36} + 344 q^{37} - 258 q^{39} + 720 q^{42} - 166 q^{43} - 1000 q^{46} + 319 q^{49} - 492 q^{51} - 24 q^{56} + 1308 q^{57} + 538 q^{58} + 73 q^{63} - 52568 q^{64} - 586 q^{67} + 2296 q^{72} - 5388 q^{74} - 2829 q^{77} - 1272 q^{78} + 1142 q^{79} - 456 q^{81} - 48 q^{84} + 11268 q^{86} - 1294 q^{88} + 1574 q^{91} - 13830 q^{92} + 3930 q^{93} + 6786 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1575, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)