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Properties

Label 675.4.bg
Level $675$
Weight $4$
Character orbit 675.bg
Rep. character $\chi_{675}(4,\cdot)$
Character field $\Q(\zeta_{90})$
Dimension $6432$
Sturm bound $360$

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Defining parameters

Level: \( N \) \(=\) \( 675 = 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 675.bg (of order \(90\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 675 \)
Character field: \(\Q(\zeta_{90})\)
Sturm bound: \(360\)

Dimensions

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

Total New Old
Modular forms 6528 6528 0
Cusp forms 6432 6432 0
Eisenstein series 96 96 0

Trace form

\( 6432 q - 30 q^{2} - 30 q^{3} - 18 q^{4} - 72 q^{5} - 18 q^{6} - 15 q^{8} - 18 q^{9} + O(q^{10}) \) \( 6432 q - 30 q^{2} - 30 q^{3} - 18 q^{4} - 72 q^{5} - 18 q^{6} - 15 q^{8} - 18 q^{9} - 12 q^{10} - 18 q^{11} - 30 q^{12} - 30 q^{13} - 18 q^{14} + 606 q^{15} + 30 q^{16} - 15 q^{17} - 9 q^{19} + 153 q^{20} - 162 q^{21} - 30 q^{22} - 30 q^{23} + 114 q^{24} - 888 q^{25} - 7584 q^{26} - 30 q^{27} - 60 q^{28} - 18 q^{29} - 447 q^{30} - 126 q^{31} - 30 q^{33} + 30 q^{34} + 402 q^{35} - 3090 q^{36} - 15 q^{37} - 30 q^{38} + 402 q^{39} + 159 q^{40} - 18 q^{41} + 1020 q^{42} + 2631 q^{44} + 3372 q^{45} - 9 q^{46} + 2820 q^{47} + 4770 q^{48} - 48 q^{49} + 4638 q^{50} + 114 q^{51} - 270 q^{52} - 60 q^{53} - 1674 q^{54} - 48 q^{55} - 3201 q^{56} - 30 q^{58} + 1476 q^{59} + 5490 q^{60} - 18 q^{61} - 15 q^{62} - 30 q^{63} - 48777 q^{64} - 3000 q^{65} + 5517 q^{66} + 9150 q^{67} - 18 q^{69} - 4116 q^{70} - 5973 q^{71} - 30 q^{72} - 15 q^{73} - 6342 q^{74} + 1686 q^{75} - 432 q^{76} + 16290 q^{77} - 9225 q^{78} - 18 q^{79} + 2934 q^{80} - 2070 q^{81} - 30 q^{83} + 6384 q^{84} + 351 q^{85} + 8322 q^{86} + 12420 q^{87} - 30 q^{88} + 6639 q^{89} - 6276 q^{90} - 9 q^{91} + 18690 q^{92} - 18 q^{94} - 4221 q^{95} + 3054 q^{96} - 30 q^{97} - 15 q^{98} - 108 q^{99} + O(q^{100}) \)

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.