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Properties

Label 675.4.bi
Level $675$
Weight $4$
Character orbit 675.bi
Rep. character $\chi_{675}(2,\cdot)$
Character field $\Q(\zeta_{180})$
Dimension $12864$
Sturm bound $360$

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Defining parameters

Level: \( N \) \(=\) \( 675 = 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 675.bi (of order \(180\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 675 \)
Character field: \(\Q(\zeta_{180})\)
Sturm bound: \(360\)

Dimensions

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

Total New Old
Modular forms 13056 13056 0
Cusp forms 12864 12864 0
Eisenstein series 192 192 0

Trace form

\( 12864 q - 48 q^{2} - 48 q^{3} - 60 q^{4} - 48 q^{5} - 36 q^{6} - 48 q^{7} - 72 q^{8} - 60 q^{9} + O(q^{10}) \) \( 12864 q - 48 q^{2} - 48 q^{3} - 60 q^{4} - 48 q^{5} - 36 q^{6} - 48 q^{7} - 72 q^{8} - 60 q^{9} - 24 q^{10} - 36 q^{11} - 48 q^{12} - 48 q^{13} - 60 q^{14} - 48 q^{15} - 36 q^{16} - 72 q^{17} - 762 q^{18} - 30 q^{19} - 816 q^{20} - 36 q^{21} - 48 q^{22} + 264 q^{23} + 1680 q^{25} + 840 q^{27} - 96 q^{28} - 60 q^{29} + 960 q^{30} - 36 q^{31} - 1812 q^{32} - 576 q^{33} - 60 q^{34} - 2556 q^{35} - 36 q^{36} - 24 q^{37} + 72 q^{38} - 60 q^{39} + 336 q^{40} - 36 q^{41} + 96 q^{42} - 48 q^{43} - 90 q^{44} + 1272 q^{45} - 18 q^{46} + 3420 q^{47} + 3168 q^{48} + 624 q^{50} - 96 q^{51} + 336 q^{52} - 60 q^{54} - 96 q^{55} - 36 q^{56} - 1902 q^{57} - 48 q^{58} - 5040 q^{59} - 15984 q^{60} - 36 q^{61} - 72 q^{62} - 2652 q^{63} - 30 q^{64} - 2136 q^{65} - 36 q^{66} - 3720 q^{67} + 8784 q^{68} - 60 q^{69} - 48 q^{70} - 54 q^{71} - 1968 q^{72} - 24 q^{73} - 9360 q^{75} + 672 q^{76} - 29376 q^{77} + 2166 q^{78} - 60 q^{79} - 36 q^{81} - 96 q^{82} + 2772 q^{83} - 60 q^{84} - 48 q^{85} - 36 q^{86} + 8580 q^{87} + 2976 q^{88} - 90 q^{89} + 14472 q^{90} - 18 q^{91} + 1878 q^{92} - 6864 q^{93} - 60 q^{94} + 4242 q^{95} - 36 q^{96} - 6960 q^{97} + 5742 q^{98} + O(q^{100}) \)

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.