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Properties

Label 1575.2.i
Level $1575$
Weight $2$
Character orbit 1575.i
Rep. character $\chi_{1575}(526,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $228$
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.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
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 504 228 276
Cusp forms 456 228 228
Eisenstein series 48 0 48

Trace form

\( 228 q - 2 q^{2} - 114 q^{4} - 8 q^{6} - 8 q^{9} + O(q^{10}) \) \( 228 q - 2 q^{2} - 114 q^{4} - 8 q^{6} - 8 q^{9} + 8 q^{11} + 32 q^{12} + 4 q^{14} - 114 q^{16} - 12 q^{17} - 26 q^{18} - 12 q^{19} + 2 q^{21} + 6 q^{22} - 12 q^{23} + 48 q^{24} + 56 q^{26} - 12 q^{27} + 22 q^{29} - 6 q^{31} - 12 q^{32} + 24 q^{33} + 18 q^{34} - 2 q^{36} + 12 q^{37} + 18 q^{38} - 20 q^{39} + 6 q^{41} - 20 q^{42} + 6 q^{43} - 100 q^{44} - 24 q^{46} - 30 q^{47} - 14 q^{48} - 114 q^{49} + 50 q^{51} + 18 q^{52} + 56 q^{53} - 20 q^{54} + 12 q^{56} + 46 q^{57} + 18 q^{58} + 52 q^{59} + 24 q^{62} + 168 q^{64} - 130 q^{66} + 92 q^{68} - 28 q^{69} - 84 q^{71} + 28 q^{72} - 36 q^{73} + 4 q^{74} + 30 q^{76} - 8 q^{77} + 8 q^{78} - 6 q^{79} - 92 q^{81} - 96 q^{82} - 10 q^{83} - 30 q^{84} - 8 q^{86} + 4 q^{87} + 42 q^{88} + 100 q^{89} + 12 q^{91} - 86 q^{92} - 30 q^{93} + 42 q^{94} + 68 q^{96} + 36 q^{97} + 4 q^{98} - 52 q^{99} + O(q^{100}) \)

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

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