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Properties

Label 1575.4.cs
Level $1575$
Weight $4$
Character orbit 1575.cs
Rep. character $\chi_{1575}(46,\cdot)$
Character field $\Q(\zeta_{15})$
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.cs (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 175 \)
Character field: \(\Q(\zeta_{15})\)
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

\( 2384 q + 3 q^{2} + 1181 q^{4} - 32 q^{7} - 82 q^{8} + O(q^{10}) \) \( 2384 q + 3 q^{2} + 1181 q^{4} - 32 q^{7} - 82 q^{8} - 35 q^{10} - 39 q^{11} - 12 q^{13} - 84 q^{14} + 4685 q^{16} + 243 q^{17} + 149 q^{19} + 636 q^{20} - 140 q^{22} + 59 q^{23} + 174 q^{25} + 1240 q^{26} + 1060 q^{28} + 60 q^{29} + 783 q^{31} - 884 q^{32} - 876 q^{34} + 114 q^{35} + 45 q^{37} - 888 q^{38} + 367 q^{40} + 1036 q^{41} - 8 q^{43} + 691 q^{44} - 263 q^{46} + 427 q^{47} + 644 q^{49} - 6654 q^{50} + 1514 q^{52} - 757 q^{53} - 1878 q^{55} + 3558 q^{56} + 1073 q^{58} - 1905 q^{59} + 1057 q^{61} - 5932 q^{62} - 31802 q^{64} - 147 q^{65} + 83 q^{67} - 6346 q^{68} + 1375 q^{70} - 3496 q^{71} + 1677 q^{73} - 1454 q^{74} + 12452 q^{76} + 3509 q^{77} - 419 q^{79} - 6056 q^{80} - 2488 q^{82} + 7864 q^{83} - 3190 q^{85} + 2975 q^{86} + 1456 q^{88} - 93 q^{89} + 876 q^{91} + 6506 q^{92} + 1373 q^{94} - 570 q^{95} + 8976 q^{97} + 5144 q^{98} + O(q^{100}) \)

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

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