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Properties

Label 1575.2.cs
Level $1575$
Weight $2$
Character orbit 1575.cs
Rep. character $\chi_{1575}(46,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $784$
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.cs (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 175 \)
Character field: \(\Q(\zeta_{15})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 1984 816 1168
Cusp forms 1856 784 1072
Eisenstein series 128 32 96

Trace form

\( 784 q + 3 q^{2} + 93 q^{4} + 5 q^{5} - 14 q^{7} + 38 q^{8} + O(q^{10}) \) \( 784 q + 3 q^{2} + 93 q^{4} + 5 q^{5} - 14 q^{7} + 38 q^{8} - 7 q^{10} - 12 q^{13} - 6 q^{14} + 93 q^{16} + 3 q^{17} - 11 q^{19} + 32 q^{20} + 12 q^{22} + 5 q^{23} - 7 q^{25} - 44 q^{26} - 38 q^{28} - 9 q^{31} + 40 q^{32} + 28 q^{34} - 8 q^{35} + 11 q^{37} + 10 q^{38} + q^{40} - 2 q^{41} + 36 q^{43} + 23 q^{44} - 43 q^{46} + 5 q^{47} - 6 q^{49} + 82 q^{50} - 70 q^{52} + 23 q^{53} - 52 q^{55} + 60 q^{56} - 59 q^{58} + 15 q^{59} - 13 q^{61} + 92 q^{62} - 214 q^{64} - q^{65} - 45 q^{67} + 122 q^{68} - 53 q^{70} + 10 q^{71} + 47 q^{73} + 22 q^{74} - 228 q^{76} - 9 q^{77} + q^{79} + 70 q^{80} + 28 q^{82} + 26 q^{83} - 98 q^{85} + 41 q^{86} - 14 q^{88} + 42 q^{89} - 38 q^{91} + 154 q^{92} - 43 q^{94} + 57 q^{95} - 168 q^{97} - 106 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1575, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 2}\)