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Properties

Label 1575.2.bx
Level $1575$
Weight $2$
Character orbit 1575.bx
Rep. character $\chi_{1575}(64,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $296$
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.bx (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 992 296 696
Cusp forms 928 296 632
Eisenstein series 64 0 64

Trace form

\( 296 q + 72 q^{4} + 10 q^{5} + O(q^{10}) \) \( 296 q + 72 q^{4} + 10 q^{5} + 8 q^{10} - 8 q^{11} + 4 q^{14} - 44 q^{16} - 12 q^{19} - 70 q^{22} + 10 q^{23} + 40 q^{25} + 12 q^{26} + 22 q^{29} + 12 q^{31} - 12 q^{34} + 2 q^{35} - 10 q^{37} + 70 q^{38} + 126 q^{40} + 4 q^{41} + 62 q^{44} + 20 q^{46} + 90 q^{47} - 296 q^{49} - 94 q^{50} - 20 q^{53} + 6 q^{55} - 12 q^{56} + 130 q^{58} - 18 q^{59} + 20 q^{61} + 50 q^{62} + 36 q^{64} - 98 q^{65} - 70 q^{67} - 8 q^{70} - 24 q^{71} - 40 q^{73} - 44 q^{74} - 12 q^{76} - 20 q^{77} - 48 q^{79} - 80 q^{80} - 30 q^{83} - 52 q^{85} - 100 q^{86} - 140 q^{88} - 2 q^{89} + 8 q^{91} + 120 q^{92} - 54 q^{95} - 30 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1575, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 2}\)