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Properties

Label 1575.4.q
Level $1575$
Weight $4$
Character orbit 1575.q
Rep. character $\chi_{1575}(316,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $896$
Sturm bound $960$

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Defining parameters

Level: \( N \) \(=\) \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1575.q (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1575, [\chi])\).

Total New Old
Modular forms 2912 896 2016
Cusp forms 2848 896 1952
Eisenstein series 64 0 64

Trace form

\( 896 q - 4 q^{2} - 888 q^{4} - 40 q^{5} - 48 q^{8} + O(q^{10}) \) \( 896 q - 4 q^{2} - 888 q^{4} - 40 q^{5} - 48 q^{8} - 92 q^{10} - 88 q^{11} - 240 q^{13} - 56 q^{14} - 3704 q^{16} + 88 q^{17} - 72 q^{19} + 580 q^{20} + 258 q^{22} + 204 q^{23} - 1080 q^{25} + 92 q^{26} - 668 q^{29} + 72 q^{31} + 992 q^{32} + 228 q^{34} - 28 q^{35} + 96 q^{37} - 818 q^{38} + 4786 q^{40} - 1056 q^{41} - 392 q^{43} - 1678 q^{44} - 280 q^{46} + 1660 q^{47} + 43904 q^{49} - 974 q^{50} - 1024 q^{52} + 1528 q^{53} - 2564 q^{55} - 672 q^{56} + 2786 q^{58} - 588 q^{59} - 200 q^{61} - 2 q^{62} - 16104 q^{64} - 3708 q^{65} + 2636 q^{67} - 376 q^{68} + 252 q^{70} - 2164 q^{71} + 2376 q^{73} + 8876 q^{74} - 2212 q^{76} - 336 q^{77} + 2292 q^{79} + 7100 q^{80} - 9776 q^{82} - 1132 q^{83} + 1308 q^{85} - 2600 q^{86} - 3236 q^{88} + 3608 q^{89} + 728 q^{91} - 18860 q^{92} - 8840 q^{94} - 4924 q^{95} - 5056 q^{97} - 196 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1575, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{4}^{\mathrm{old}}(1575, [\chi])\) into lower level spaces

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