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Properties

Label 2450.4.bt
Level $2450$
Weight $4$
Character orbit 2450.bt
Rep. character $\chi_{2450}(9,\cdot)$
Character field $\Q(\zeta_{210})$
Dimension $20160$
Sturm bound $1680$

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Defining parameters

Level: \( N \) \(=\) \( 2450 = 2 \cdot 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2450.bt (of order \(210\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1225 \)
Character field: \(\Q(\zeta_{210})\)
Sturm bound: \(1680\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(2450, [\chi])\).

Total New Old
Modular forms 60672 20160 40512
Cusp forms 60288 20160 40128
Eisenstein series 384 0 384

Trace form

\( 20160 q + 1680 q^{4} - 8 q^{5} + 48 q^{6} + 3780 q^{9} + O(q^{10}) \) \( 20160 q + 1680 q^{4} - 8 q^{5} + 48 q^{6} + 3780 q^{9} + 12 q^{10} + 672 q^{11} + 378 q^{15} - 6720 q^{16} - 1600 q^{17} - 456 q^{19} + 160 q^{20} + 48 q^{21} - 70 q^{23} - 384 q^{24} + 154 q^{25} + 1248 q^{26} + 2640 q^{27} - 120 q^{28} - 84 q^{30} + 414 q^{31} - 1600 q^{33} - 544 q^{34} - 484 q^{35} + 30240 q^{36} - 280 q^{39} + 624 q^{40} + 1888 q^{41} - 1020 q^{42} + 224 q^{44} + 3000 q^{45} + 276 q^{49} + 336 q^{50} - 588 q^{51} + 864 q^{54} + 3704 q^{55} + 216 q^{59} - 8400 q^{60} - 1388 q^{61} + 8400 q^{62} + 2000 q^{63} - 53760 q^{64} + 826 q^{65} - 1600 q^{66} - 5904 q^{69} - 520 q^{70} + 13860 q^{71} - 2280 q^{73} + 10554 q^{75} - 2432 q^{76} - 5440 q^{77} + 336 q^{79} - 128 q^{80} - 32228 q^{81} + 4160 q^{83} - 1728 q^{84} - 3668 q^{85} - 1344 q^{86} + 1680 q^{88} - 30504 q^{89} - 7408 q^{90} - 696 q^{91} + 1600 q^{94} - 9450 q^{95} - 384 q^{96} - 1860 q^{97} + 3280 q^{98} - 5040 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(2450, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(2450, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(2450, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(1225, [\chi])\)\(^{\oplus 2}\)