Properties

Label 450.4.v
Level $450$
Weight $4$
Character orbit 450.v
Rep. character $\chi_{450}(79,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $720$
Sturm bound $360$

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Defining parameters

Level: \( N \) \(=\) \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 450.v (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 225 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(360\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(450, [\chi])\).

Total New Old
Modular forms 2192 720 1472
Cusp forms 2128 720 1408
Eisenstein series 64 0 64

Trace form

\( 720 q - 360 q^{4} - 32 q^{5} + 64 q^{9} + O(q^{10}) \) \( 720 q - 360 q^{4} - 32 q^{5} + 64 q^{9} + 44 q^{11} - 80 q^{12} - 112 q^{14} + 406 q^{15} + 1440 q^{16} - 32 q^{20} + 96 q^{21} - 576 q^{25} + 2496 q^{26} + 660 q^{27} - 348 q^{29} + 188 q^{30} - 72 q^{31} - 1600 q^{33} - 572 q^{35} + 512 q^{36} - 172 q^{39} + 656 q^{41} + 352 q^{44} + 1146 q^{45} + 1900 q^{47} + 640 q^{48} + 17640 q^{49} + 488 q^{50} - 68 q^{51} - 1104 q^{54} + 180 q^{55} + 448 q^{56} + 288 q^{59} - 1944 q^{60} - 4920 q^{62} - 5560 q^{63} + 11520 q^{64} - 1474 q^{65} - 544 q^{66} - 3060 q^{67} - 68 q^{69} - 144 q^{70} + 3064 q^{71} + 5920 q^{74} + 4878 q^{75} - 5440 q^{77} + 6640 q^{78} + 252 q^{79} - 256 q^{80} + 696 q^{81} + 280 q^{83} - 288 q^{84} - 828 q^{85} + 1720 q^{86} + 4200 q^{87} - 4528 q^{89} - 8524 q^{90} - 5680 q^{92} - 2772 q^{95} - 2848 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(450, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(450, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(450, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 2}\)