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Properties

Label 675.4.bc
Level $675$
Weight $4$
Character orbit 675.bc
Rep. character $\chi_{675}(16,\cdot)$
Character field $\Q(\zeta_{45})$
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.bc (of order \(45\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 675 \)
Character field: \(\Q(\zeta_{45})\)
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

\( 6432 q - 18 q^{2} - 18 q^{3} - 18 q^{4} + 24 q^{5} - 18 q^{6} - 48 q^{7} - 9 q^{8} - 18 q^{9} + O(q^{10}) \) \( 6432 q - 18 q^{2} - 18 q^{3} - 18 q^{4} + 24 q^{5} - 18 q^{6} - 48 q^{7} - 9 q^{8} - 18 q^{9} - 12 q^{10} - 18 q^{11} - 18 q^{12} - 18 q^{13} - 18 q^{14} - 654 q^{15} - 66 q^{16} - 9 q^{17} + 666 q^{18} - 9 q^{19} + 567 q^{20} + 126 q^{21} - 18 q^{22} - 330 q^{23} - 210 q^{24} - 888 q^{25} + 7392 q^{26} - 906 q^{27} - 36 q^{28} - 18 q^{29} - 609 q^{30} + 90 q^{31} + 948 q^{32} - 546 q^{33} - 66 q^{34} + 402 q^{35} + 3054 q^{36} - 9 q^{37} + 6 q^{38} + 402 q^{39} - 591 q^{40} - 18 q^{41} + 2436 q^{42} - 48 q^{43} + 2631 q^{44} - 2100 q^{45} - 9 q^{46} - 4056 q^{47} - 4194 q^{48} - 48 q^{49} - 4014 q^{50} - 210 q^{51} - 162 q^{52} - 1716 q^{53} - 1674 q^{54} - 48 q^{55} + 3165 q^{56} - 2226 q^{57} - 18 q^{58} + 1476 q^{59} + 7806 q^{60} - 18 q^{61} - 9 q^{62} + 2586 q^{63} + 48759 q^{64} + 5040 q^{65} - 5553 q^{66} - 5526 q^{67} - 9648 q^{68} - 18 q^{69} + 4068 q^{70} + 5955 q^{71} - 4242 q^{72} - 9 q^{73} - 6438 q^{74} - 1134 q^{75} - 432 q^{76} + 6558 q^{77} + 255 q^{78} - 18 q^{79} - 3210 q^{80} + 2034 q^{81} - 96 q^{82} + 2802 q^{83} + 7032 q^{84} - 399 q^{85} - 8358 q^{86} - 11136 q^{87} - 3138 q^{88} + 6159 q^{89} + 12000 q^{90} - 9 q^{91} - 1836 q^{92} + 17856 q^{93} - 18 q^{94} + 6963 q^{95} - 3090 q^{96} + 6894 q^{97} - 1947 q^{98} - 108 q^{99} + O(q^{100}) \)

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.