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Properties

Label 1575.2.bf
Level $1575$
Weight $2$
Character orbit 1575.bf
Rep. character $\chi_{1575}(551,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $292$
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.bf (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
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 504 316 188
Cusp forms 456 292 164
Eisenstein series 48 24 24

Trace form

\( 292 q + 3 q^{2} + 3 q^{3} + 139 q^{4} + 6 q^{6} - 3 q^{9} + O(q^{10}) \) \( 292 q + 3 q^{2} + 3 q^{3} + 139 q^{4} + 6 q^{6} - 3 q^{9} + 3 q^{12} + 3 q^{13} - 3 q^{14} - 123 q^{16} + 9 q^{17} - q^{18} + 6 q^{19} - 18 q^{21} - 2 q^{22} + 12 q^{24} + 18 q^{26} - 9 q^{27} + 10 q^{28} + 24 q^{29} - 21 q^{31} - 39 q^{32} + 30 q^{33} - 18 q^{34} - 60 q^{36} + 3 q^{37} + 66 q^{38} - 18 q^{39} + 6 q^{41} + 21 q^{42} + 6 q^{43} + 15 q^{44} - 4 q^{46} + 21 q^{47} - 45 q^{48} + 14 q^{49} - 18 q^{51} - 24 q^{53} - 42 q^{54} - 18 q^{56} + 21 q^{57} - 2 q^{58} - 12 q^{59} - 6 q^{61} - 24 q^{62} - 20 q^{63} - 180 q^{64} + 45 q^{66} - 8 q^{67} + 108 q^{68} + 48 q^{69} + 49 q^{72} + 6 q^{73} + 48 q^{76} + 6 q^{77} + 9 q^{78} - 14 q^{79} + 21 q^{81} - 30 q^{83} - 69 q^{84} + 63 q^{87} - 22 q^{88} - 27 q^{89} + 5 q^{91} - 42 q^{92} + 48 q^{93} + 3 q^{94} - 126 q^{96} + 3 q^{97} + 33 q^{98} - 6 q^{99} + O(q^{100}) \)

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

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