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Properties

Label 450.3.t
Level $450$
Weight $3$
Character orbit 450.t
Rep. character $\chi_{450}(11,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $480$
Sturm bound $270$

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Defining parameters

Level: \( N \) \(=\) \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 450.t (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 225 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(270\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(450, [\chi])\).

Total New Old
Modular forms 1472 480 992
Cusp forms 1408 480 928
Eisenstein series 64 0 64

Trace form

\( 480 q + 4 q^{3} - 120 q^{4} - 72 q^{5} - 20 q^{9} + O(q^{10}) \) \( 480 q + 4 q^{3} - 120 q^{4} - 72 q^{5} - 20 q^{9} + 12 q^{12} - 78 q^{15} + 240 q^{16} + 32 q^{18} + 36 q^{20} + 120 q^{21} - 144 q^{23} - 24 q^{25} - 86 q^{27} - 92 q^{30} - 60 q^{31} + 106 q^{33} - 80 q^{36} - 168 q^{37} + 216 q^{38} + 80 q^{39} - 32 q^{42} - 506 q^{45} + 126 q^{47} + 48 q^{48} - 1680 q^{49} + 20 q^{51} - 240 q^{54} + 108 q^{55} + 324 q^{57} - 48 q^{58} + 270 q^{59} + 136 q^{60} + 490 q^{63} + 960 q^{64} - 270 q^{65} + 160 q^{66} - 234 q^{67} + 864 q^{68} + 220 q^{69} - 192 q^{70} + 128 q^{72} - 728 q^{75} + 144 q^{77} - 124 q^{78} - 120 q^{79} + 220 q^{81} - 96 q^{82} + 360 q^{83} - 180 q^{84} - 48 q^{85} - 1162 q^{87} - 200 q^{90} + 432 q^{92} - 468 q^{93} + 180 q^{95} - 12 q^{97} - 780 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(450, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(450, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(450, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 2}\)