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Properties

Label 675.4.l
Level $675$
Weight $4$
Character orbit 675.l
Rep. character $\chi_{675}(76,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $1008$
Sturm bound $360$

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Defining parameters

Level: \( N \) \(=\) \( 675 = 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 675.l (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 27 \)
Character field: \(\Q(\zeta_{9})\)
Sturm bound: \(360\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(675, [\chi])\).

Total New Old
Modular forms 1656 1044 612
Cusp forms 1584 1008 576
Eisenstein series 72 36 36

Trace form

\( 1008 q + 6 q^{2} + 6 q^{3} + 6 q^{4} - 6 q^{6} + 6 q^{7} - 69 q^{8} + 54 q^{9} + O(q^{10}) \) \( 1008 q + 6 q^{2} + 6 q^{3} + 6 q^{4} - 6 q^{6} + 6 q^{7} - 69 q^{8} + 54 q^{9} + 69 q^{11} + 159 q^{12} + 6 q^{13} - 201 q^{14} - 42 q^{16} - 201 q^{17} + 87 q^{18} + 3 q^{19} - 6 q^{21} - 48 q^{22} + 102 q^{23} + 1344 q^{24} + 18 q^{26} + 249 q^{27} + 12 q^{28} + 240 q^{29} + 36 q^{31} + 360 q^{32} - 1155 q^{33} + 348 q^{34} - 36 q^{36} + 3 q^{37} - 1488 q^{38} + 768 q^{39} + 1497 q^{41} - 1662 q^{42} + 519 q^{43} + 2211 q^{44} - 9 q^{46} - 192 q^{47} + 2925 q^{48} + 600 q^{49} + 4221 q^{51} - 1323 q^{52} + 1080 q^{53} - 5094 q^{54} - 7131 q^{56} + 1260 q^{57} - 885 q^{58} + 2082 q^{59} - 72 q^{61} - 2112 q^{62} + 6 q^{63} - 28221 q^{64} + 2451 q^{66} + 3003 q^{67} - 9237 q^{68} + 858 q^{69} + 2853 q^{71} - 4248 q^{72} - 213 q^{73} - 6387 q^{74} + 3798 q^{76} - 5010 q^{77} - 1224 q^{78} - 2802 q^{79} + 378 q^{81} + 12 q^{82} + 6300 q^{83} - 2712 q^{84} + 4632 q^{86} + 4224 q^{87} - 258 q^{88} + 1452 q^{89} + 261 q^{91} - 1539 q^{92} + 6114 q^{93} + 5703 q^{94} - 3270 q^{96} + 3543 q^{97} - 6324 q^{98} + 9702 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(675, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{4}^{\mathrm{old}}(675, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(675, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 2}\)