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Properties

Label 2450.4.x
Level $2450$
Weight $4$
Character orbit 2450.x
Rep. character $\chi_{2450}(51,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $3192$
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.x (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{21})\)
Sturm bound: \(1680\)

Dimensions

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

Total New Old
Modular forms 15264 3192 12072
Cusp forms 14976 3192 11784
Eisenstein series 288 0 288

Trace form

\( 3192 q - 6 q^{3} + 1064 q^{4} - 44 q^{6} + 52 q^{7} + 2506 q^{9} + O(q^{10}) \) \( 3192 q - 6 q^{3} + 1064 q^{4} - 44 q^{6} + 52 q^{7} + 2506 q^{9} + 210 q^{11} - 24 q^{12} + 8 q^{13} + 64 q^{14} + 4256 q^{16} + 206 q^{17} + 56 q^{18} + 92 q^{19} + 318 q^{21} + 476 q^{22} + 658 q^{23} + 32 q^{24} + 724 q^{26} + 1296 q^{27} - 8 q^{28} + 434 q^{29} + 342 q^{31} - 378 q^{33} - 512 q^{34} - 18872 q^{36} + 3332 q^{37} + 1296 q^{38} + 4942 q^{39} - 568 q^{41} - 884 q^{42} + 1512 q^{43} + 840 q^{44} + 3472 q^{46} - 1560 q^{47} - 1152 q^{48} + 4628 q^{49} + 4242 q^{51} - 1920 q^{52} + 518 q^{53} + 1208 q^{54} - 448 q^{56} + 1876 q^{57} - 504 q^{58} - 916 q^{59} + 16832 q^{61} + 3384 q^{62} + 2148 q^{63} - 34048 q^{64} + 2240 q^{66} + 182 q^{67} + 936 q^{68} + 2904 q^{69} + 2436 q^{71} + 224 q^{72} + 1734 q^{73} + 2772 q^{74} - 2864 q^{76} + 2934 q^{77} - 1904 q^{78} + 1750 q^{79} + 28896 q^{81} + 624 q^{82} - 2432 q^{83} + 1080 q^{84} + 1428 q^{86} + 8030 q^{87} - 560 q^{88} + 10290 q^{89} + 470 q^{91} - 560 q^{92} + 15750 q^{93} - 7124 q^{94} + 128 q^{96} - 2228 q^{97} - 6616 q^{98} - 19096 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(2450, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(490, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(1225, [\chi])\)\(^{\oplus 2}\)