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Properties

Label 1575.2.q
Level $1575$
Weight $2$
Character orbit 1575.q
Rep. character $\chi_{1575}(316,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $304$
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.q (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1575, [\chi])\).

Total New Old
Modular forms 992 304 688
Cusp forms 928 304 624
Eisenstein series 64 0 64

Trace form

\( 304 q - 2 q^{2} - 78 q^{4} - 12 q^{5} - 6 q^{8} + O(q^{10}) \) \( 304 q - 2 q^{2} - 78 q^{4} - 12 q^{5} - 6 q^{8} + 6 q^{10} + 8 q^{11} + 4 q^{14} - 106 q^{16} - 16 q^{17} - 12 q^{19} + 52 q^{20} + 34 q^{22} + 18 q^{23} + 2 q^{25} - 32 q^{26} + 2 q^{29} - 12 q^{31} + 56 q^{32} + 18 q^{34} - 2 q^{35} + 8 q^{37} - 46 q^{38} - 36 q^{40} - 24 q^{41} + 36 q^{43} + 62 q^{44} - 20 q^{46} + 10 q^{47} + 304 q^{49} + 76 q^{50} + 28 q^{52} + 46 q^{53} + 94 q^{55} + 12 q^{56} + 2 q^{58} - 18 q^{59} - 40 q^{61} + 74 q^{62} - 114 q^{64} + 28 q^{65} + 18 q^{67} - 12 q^{68} + 16 q^{70} + 64 q^{71} - 68 q^{73} - 64 q^{74} + 12 q^{76} + 12 q^{77} - 48 q^{79} - 138 q^{80} - 148 q^{82} + 6 q^{83} - 14 q^{85} + 100 q^{86} - 132 q^{88} + 68 q^{89} - 8 q^{91} + 40 q^{92} + 40 q^{94} + 122 q^{95} - 18 q^{97} - 2 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1575, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 4}\)