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Properties

Label 1575.2.u
Level $1575$
Weight $2$
Character orbit 1575.u
Rep. character $\chi_{1575}(101,\cdot)$
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.u (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

\( 292 q + 3 q^{3} - 278 q^{4} - 6 q^{6} + 3 q^{9} + O(q^{10}) \) \( 292 q + 3 q^{3} - 278 q^{4} - 6 q^{6} + 3 q^{9} - 3 q^{11} - 18 q^{12} - 3 q^{13} + 12 q^{14} + 246 q^{16} - 9 q^{17} + 2 q^{18} + 6 q^{19} + 9 q^{21} - 2 q^{22} + 24 q^{23} + 42 q^{24} - 18 q^{26} + 9 q^{27} + 10 q^{28} + 24 q^{29} + 3 q^{33} + 18 q^{34} - 60 q^{36} + 3 q^{37} + 33 q^{38} - 15 q^{39} - 6 q^{41} + 24 q^{42} + 6 q^{43} - 15 q^{44} - 4 q^{46} + 42 q^{47} + 45 q^{48} - 4 q^{49} - 36 q^{51} + 39 q^{52} + 24 q^{53} - 39 q^{54} - 48 q^{56} + 21 q^{57} + q^{58} - 24 q^{59} + 24 q^{62} + 91 q^{63} - 180 q^{64} - 72 q^{66} + 16 q^{67} + 54 q^{68} - 48 q^{69} - 32 q^{72} + 6 q^{73} - 21 q^{74} - 48 q^{76} + 6 q^{77} + 9 q^{78} + 28 q^{79} - 21 q^{81} + 30 q^{83} - 21 q^{84} - 117 q^{86} - 15 q^{87} + 11 q^{88} + 27 q^{89} + 5 q^{91} - 42 q^{92} - 66 q^{93} - 135 q^{96} - 3 q^{97} - 33 q^{98} - 6 q^{99} + O(q^{100}) \)

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

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