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Properties

Label 495.4.bg
Level $495$
Weight $4$
Character orbit 495.bg
Rep. character $\chi_{495}(16,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $1152$
Sturm bound $288$

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Defining parameters

Level: \( N \) \(=\) \( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 495.bg (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 99 \)
Character field: \(\Q(\zeta_{15})\)
Sturm bound: \(288\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(495, [\chi])\).

Total New Old
Modular forms 1760 1152 608
Cusp forms 1696 1152 544
Eisenstein series 64 0 64

Trace form

\( 1152 q - 8 q^{2} + 4 q^{3} + 576 q^{4} - 60 q^{6} + 192 q^{8} - 156 q^{9} + O(q^{10}) \) \( 1152 q - 8 q^{2} + 4 q^{3} + 576 q^{4} - 60 q^{6} + 192 q^{8} - 156 q^{9} - 46 q^{11} - 96 q^{12} - 60 q^{15} + 2304 q^{16} + 1000 q^{17} + 328 q^{18} + 540 q^{19} + 32 q^{21} + 36 q^{22} + 168 q^{23} - 1088 q^{24} + 3600 q^{25} - 1024 q^{26} + 76 q^{27} + 56 q^{29} + 160 q^{30} + 3584 q^{32} - 788 q^{33} - 360 q^{34} + 1120 q^{35} + 1416 q^{36} + 156 q^{38} - 956 q^{39} - 1300 q^{41} + 974 q^{42} - 684 q^{43} - 7652 q^{44} + 816 q^{47} - 2568 q^{48} + 7056 q^{49} - 200 q^{50} - 2014 q^{51} - 4368 q^{53} - 1692 q^{54} - 2684 q^{56} + 5856 q^{57} + 862 q^{59} + 2110 q^{60} + 624 q^{62} + 164 q^{63} - 18432 q^{64} + 3520 q^{65} + 4274 q^{66} - 1548 q^{67} - 9994 q^{68} + 7512 q^{69} + 5696 q^{71} + 5952 q^{72} - 4968 q^{73} + 20 q^{74} - 150 q^{75} + 2160 q^{76} + 176 q^{77} - 14184 q^{78} + 936 q^{79} - 6960 q^{80} + 1020 q^{81} - 6264 q^{82} - 4320 q^{83} - 3468 q^{84} + 720 q^{85} + 628 q^{86} + 728 q^{87} + 432 q^{88} - 14480 q^{89} - 320 q^{90} + 1512 q^{91} - 6692 q^{92} - 7736 q^{93} - 3040 q^{95} - 20370 q^{96} + 162 q^{97} - 28568 q^{98} - 9308 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(495, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(495, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(495, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 2}\)