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Properties

Label 1575.2.k
Level $1575$
Weight $2$
Character orbit 1575.k
Rep. character $\chi_{1575}(1201,\cdot)$
Character field $\Q(\zeta_{3})$
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.k (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{3})\)
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

\( 292 q - q^{2} + q^{3} - 141 q^{4} - 14 q^{6} + 2 q^{7} + 12 q^{8} + q^{9} + O(q^{10}) \) \( 292 q - q^{2} + q^{3} - 141 q^{4} - 14 q^{6} + 2 q^{7} + 12 q^{8} + q^{9} - 10 q^{11} + q^{12} + q^{13} + 25 q^{14} - 127 q^{16} + 7 q^{17} + 11 q^{18} + 4 q^{19} + 14 q^{21} + 6 q^{22} - 12 q^{23} + 12 q^{24} - 16 q^{26} + q^{27} + 14 q^{28} - 8 q^{29} - q^{31} - 13 q^{32} + 20 q^{33} + 8 q^{34} - 32 q^{36} + q^{37} - 50 q^{38} + 28 q^{39} - 30 q^{41} - 5 q^{42} - 2 q^{43} + 35 q^{44} - 8 q^{46} + 25 q^{47} + 69 q^{48} - 10 q^{49} + 14 q^{51} - 14 q^{52} + 12 q^{53} - 32 q^{54} - 24 q^{56} - 25 q^{57} - 18 q^{58} - 20 q^{59} - 10 q^{61} + 36 q^{62} - 6 q^{63} + 212 q^{64} + 53 q^{66} - 8 q^{67} - 56 q^{68} - 10 q^{69} - 66 q^{71} - 11 q^{72} + 16 q^{73} - 14 q^{74} + 18 q^{76} + 16 q^{77} - 5 q^{78} + 10 q^{79} - 35 q^{81} + 50 q^{83} - 45 q^{84} + 10 q^{86} - 7 q^{87} - 6 q^{88} - 41 q^{89} - 15 q^{91} + 70 q^{92} + 48 q^{93} + 35 q^{94} - 52 q^{96} + q^{97} - 51 q^{98} + 20 q^{99} + O(q^{100}) \)

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

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