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Properties

Label 465.4.br
Level $465$
Weight $4$
Character orbit 465.br
Rep. character $\chi_{465}(11,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $1024$
Sturm bound $256$

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Defining parameters

Level: \( N \) \(=\) \( 465 = 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 465.br (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 93 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(256\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(465, [\chi])\).

Total New Old
Modular forms 1568 1024 544
Cusp forms 1504 1024 480
Eisenstein series 64 0 64

Trace form

\( 1024 q + 1036 q^{4} + 90 q^{6} + 64 q^{7} + O(q^{10}) \) \( 1024 q + 1036 q^{4} + 90 q^{6} + 64 q^{7} - 30 q^{10} - 390 q^{12} - 252 q^{13} - 3820 q^{16} + 410 q^{18} - 100 q^{19} - 480 q^{21} - 720 q^{24} + 12800 q^{25} - 60 q^{27} + 5904 q^{28} + 280 q^{31} + 784 q^{33} + 1026 q^{34} - 510 q^{36} - 1620 q^{37} - 296 q^{39} - 1740 q^{40} + 3196 q^{42} - 152 q^{43} + 80 q^{45} - 150 q^{46} - 3564 q^{48} + 4344 q^{49} + 352 q^{51} + 8244 q^{52} + 1100 q^{54} - 360 q^{55} + 6672 q^{57} + 3780 q^{58} + 9872 q^{63} + 18988 q^{64} - 604 q^{66} - 928 q^{67} + 10956 q^{69} - 15100 q^{72} - 4524 q^{73} + 4716 q^{76} - 11144 q^{78} + 4880 q^{79} + 1264 q^{81} - 2868 q^{82} - 620 q^{84} + 56 q^{87} - 4536 q^{88} - 480 q^{90} - 19660 q^{91} - 7536 q^{93} - 16344 q^{94} - 15050 q^{96} - 10020 q^{97} - 3648 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(465, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(465, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(465, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(93, [\chi])\)\(^{\oplus 2}\)