Properties

Label 1575.4.i
Level $1575$
Weight $4$
Character orbit 1575.i
Rep. character $\chi_{1575}(526,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $684$
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.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
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 684 780
Cusp forms 1416 684 732
Eisenstein series 48 0 48

Trace form

\( 684 q + 4 q^{2} - 6 q^{3} - 1368 q^{4} + 10 q^{6} - 108 q^{8} + 94 q^{9} + O(q^{10}) \) \( 684 q + 4 q^{2} - 6 q^{3} - 1368 q^{4} + 10 q^{6} - 108 q^{8} + 94 q^{9} - 34 q^{11} + 140 q^{12} - 56 q^{14} - 5472 q^{16} - 228 q^{17} + 466 q^{18} + 180 q^{19} + 56 q^{21} - 36 q^{22} + 456 q^{23} - 1074 q^{24} + 776 q^{26} - 480 q^{27} - 260 q^{29} + 36 q^{31} + 726 q^{32} - 1722 q^{33} - 216 q^{34} - 1412 q^{36} + 144 q^{37} + 1440 q^{38} + 112 q^{39} + 186 q^{41} - 140 q^{42} + 342 q^{43} - 1936 q^{44} - 72 q^{46} - 804 q^{47} + 1684 q^{48} - 16758 q^{49} - 2422 q^{51} - 918 q^{52} - 1600 q^{53} + 802 q^{54} - 672 q^{56} - 1274 q^{57} - 594 q^{58} + 442 q^{59} - 4512 q^{62} + 588 q^{63} + 42948 q^{64} - 466 q^{66} + 162 q^{67} + 206 q^{68} + 440 q^{69} + 9024 q^{71} - 4790 q^{72} + 2484 q^{73} - 3896 q^{74} + 36 q^{76} + 616 q^{77} - 6964 q^{78} + 468 q^{79} - 1610 q^{81} + 252 q^{82} + 236 q^{83} - 1302 q^{84} - 1742 q^{86} + 8908 q^{87} - 2520 q^{88} + 4960 q^{89} - 504 q^{91} + 8758 q^{92} - 396 q^{93} - 306 q^{94} + 12500 q^{96} - 1890 q^{97} - 392 q^{98} - 3292 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1575, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)