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Properties

Label 1575.4.k
Level $1575$
Weight $4$
Character orbit 1575.k
Rep. character $\chi_{1575}(1201,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $900$
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.k (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(960\)

Dimensions

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

Total New Old
Modular forms 1464 924 540
Cusp forms 1416 900 516
Eisenstein series 48 24 24

Trace form

\( 900 q - q^{2} + q^{3} - 1777 q^{4} + 4 q^{6} - 5 q^{7} + 24 q^{8} + 31 q^{9} + O(q^{10}) \) \( 900 q - q^{2} + q^{3} - 1777 q^{4} + 4 q^{6} - 5 q^{7} + 24 q^{8} + 31 q^{9} + 2 q^{11} - 179 q^{12} - 10 q^{13} + 43 q^{14} - 6917 q^{16} - 110 q^{17} + 95 q^{18} + 62 q^{19} - 334 q^{21} + 18 q^{22} - 18 q^{23} + 42 q^{24} + 338 q^{26} - 260 q^{27} - 20 q^{28} - 248 q^{29} + 63 q^{31} - 817 q^{32} - 79 q^{33} + 26 q^{34} - 866 q^{36} - 82 q^{37} + 1462 q^{38} - 59 q^{39} + 204 q^{41} + 241 q^{42} - 82 q^{43} - 295 q^{44} + 262 q^{46} - 1007 q^{47} + 921 q^{48} + 517 q^{49} - 505 q^{51} + 98 q^{52} + 822 q^{53} - 1676 q^{54} - 1806 q^{56} + 506 q^{57} + 474 q^{58} + 1165 q^{59} + 405 q^{61} + 3828 q^{62} + 363 q^{63} + 52312 q^{64} + 1139 q^{66} + 293 q^{67} + 640 q^{68} - 3817 q^{69} + 132 q^{71} - 29 q^{72} - 334 q^{73} - 2954 q^{74} + 1162 q^{76} + 3085 q^{77} - 869 q^{78} - 553 q^{79} - 329 q^{81} - 6 q^{82} - 1408 q^{83} + 4113 q^{84} - 8294 q^{86} + 1622 q^{87} + 738 q^{88} + 2200 q^{89} + 172 q^{91} + 1096 q^{92} - 141 q^{93} + 1319 q^{94} - 1066 q^{96} - 262 q^{97} + 7893 q^{98} - 25 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1575, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)