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Properties

Label 1575.4.bf
Level $1575$
Weight $4$
Character orbit 1575.bf
Rep. character $\chi_{1575}(551,\cdot)$
Character field $\Q(\zeta_{6})$
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.bf (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
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

\( 900 q + 3 q^{2} + 3 q^{3} + 1775 q^{4} + 24 q^{6} + 7 q^{7} + 3 q^{9} + O(q^{10}) \) \( 900 q + 3 q^{2} + 3 q^{3} + 1775 q^{4} + 24 q^{6} + 7 q^{7} + 3 q^{9} + 3 q^{12} + 36 q^{13} - 129 q^{14} - 6901 q^{16} - 72 q^{17} - 13 q^{18} + 6 q^{19} + 138 q^{21} - 14 q^{22} + 390 q^{24} + 144 q^{26} + 396 q^{27} - 36 q^{28} + 132 q^{29} + 171 q^{31} + 501 q^{32} - 105 q^{33} - 72 q^{34} + 6 q^{36} + 86 q^{37} - 1734 q^{38} - 411 q^{39} + 618 q^{41} - 909 q^{42} + 86 q^{43} - 1803 q^{44} - 274 q^{46} - 195 q^{47} + 1071 q^{48} - 275 q^{49} + 159 q^{51} - 564 q^{53} + 3774 q^{54} - 2412 q^{56} - 1218 q^{57} + 538 q^{58} + 753 q^{59} - 1323 q^{61} - 2904 q^{62} - 893 q^{63} - 52040 q^{64} + 3951 q^{66} + 293 q^{67} + 2412 q^{68} - 681 q^{69} - 617 q^{72} + 6 q^{73} + 624 q^{76} - 4413 q^{77} + 537 q^{78} + 131 q^{79} - 585 q^{81} - 18 q^{82} - 1830 q^{83} + 2493 q^{84} - 1962 q^{87} - 1246 q^{88} + 4266 q^{89} + 224 q^{91} + 4116 q^{92} - 2073 q^{93} + 3 q^{94} + 4644 q^{96} + 792 q^{97} - 5619 q^{98} - 3675 q^{99} + O(q^{100}) \)

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

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