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Properties

Label 1575.4.dk
Level $1575$
Weight $4$
Character orbit 1575.dk
Rep. character $\chi_{1575}(109,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $2384$
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.dk (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 175 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(960\)

Dimensions

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

Total New Old
Modular forms 5824 2416 3408
Cusp forms 5696 2384 3312
Eisenstein series 128 32 96

Trace form

\( 2384 q + 5 q^{2} - 1187 q^{4} + 230 q^{8} + O(q^{10}) \) \( 2384 q + 5 q^{2} - 1187 q^{4} + 230 q^{8} + 3 q^{10} + 45 q^{11} - 20 q^{13} - 36 q^{14} + 4653 q^{16} + 325 q^{17} + 149 q^{19} - 348 q^{20} - 740 q^{22} - 355 q^{23} - 142 q^{25} - 1224 q^{26} + 30 q^{28} + 60 q^{29} - 789 q^{31} - 812 q^{34} + 662 q^{35} - 5 q^{37} - 1240 q^{38} + 101 q^{40} - 1012 q^{41} + 723 q^{44} + 257 q^{46} + 5 q^{47} + 644 q^{49} - 2058 q^{50} + 1710 q^{52} - 2155 q^{53} - 1222 q^{55} - 3290 q^{56} - 3425 q^{58} - 1905 q^{59} - 1063 q^{61} - 1420 q^{62} + 40806 q^{64} - 281 q^{65} + 2305 q^{67} + 1737 q^{70} + 3520 q^{71} + 2275 q^{73} - 1518 q^{74} - 13028 q^{76} + 4445 q^{77} - 419 q^{79} + 3110 q^{80} + 7080 q^{83} + 302 q^{85} - 2969 q^{86} - 7410 q^{88} - 93 q^{89} - 888 q^{91} - 13150 q^{92} + 1437 q^{94} - 1498 q^{95} + 13000 q^{97} + 16830 q^{98} + O(q^{100}) \)

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

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