Properties

Label 2450.4.l
Level $2450$
Weight $4$
Character orbit 2450.l
Rep. character $\chi_{2450}(351,\cdot)$
Character field $\Q(\zeta_{7})$
Dimension $1596$
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.l (of order \(7\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{7})\)
Sturm bound: \(1680\)

Dimensions

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

Total New Old
Modular forms 7632 1596 6036
Cusp forms 7488 1596 5892
Eisenstein series 144 0 144

Trace form

\( 1596 q - 6 q^{3} - 1064 q^{4} + 8 q^{6} - 4 q^{7} - 2464 q^{9} + O(q^{10}) \) \( 1596 q - 6 q^{3} - 1064 q^{4} + 8 q^{6} - 4 q^{7} - 2464 q^{9} - 168 q^{11} - 24 q^{12} - 74 q^{13} + 68 q^{14} - 4256 q^{16} - 344 q^{17} + 112 q^{18} + 388 q^{19} + 270 q^{21} - 476 q^{22} - 448 q^{23} - 80 q^{24} - 616 q^{26} - 288 q^{27} - 16 q^{28} - 434 q^{29} - 252 q^{31} - 936 q^{33} + 104 q^{34} - 9856 q^{36} + 322 q^{37} + 672 q^{38} + 1610 q^{39} - 896 q^{41} + 848 q^{42} - 1008 q^{43} + 504 q^{44} + 1652 q^{46} - 822 q^{47} + 576 q^{48} + 1066 q^{49} + 1428 q^{51} + 1104 q^{52} - 2492 q^{53} + 556 q^{54} + 160 q^{56} - 2548 q^{57} + 2520 q^{58} - 1556 q^{59} + 2764 q^{61} + 2124 q^{62} + 468 q^{63} - 17024 q^{64} - 224 q^{66} - 1148 q^{67} - 1488 q^{68} - 1836 q^{69} - 2436 q^{71} + 448 q^{72} - 996 q^{73} - 2100 q^{74} + 488 q^{76} - 2316 q^{77} + 1904 q^{78} + 980 q^{79} - 18312 q^{81} - 504 q^{82} - 1630 q^{83} + 408 q^{84} + 1092 q^{86} - 3650 q^{87} + 1232 q^{88} - 11400 q^{89} + 2896 q^{91} + 560 q^{92} + 168 q^{93} + 3548 q^{94} - 320 q^{96} - 8608 q^{97} + 4792 q^{98} + 19096 q^{99} + O(q^{100}) \)

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

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