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Properties

Label 2450.2.bj
Level $2450$
Weight $2$
Character orbit 2450.bj
Rep. character $\chi_{2450}(29,\cdot)$
Character field $\Q(\zeta_{70})$
Dimension $3360$
Sturm bound $840$

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Defining parameters

Level: \( N \) \(=\) \( 2450 = 2 \cdot 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2450.bj (of order \(70\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1225 \)
Character field: \(\Q(\zeta_{70})\)
Sturm bound: \(840\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2450, [\chi])\).

Total New Old
Modular forms 10176 3360 6816
Cusp forms 9984 3360 6624
Eisenstein series 192 0 192

Trace form

\( 3360 q - 140 q^{4} + 4 q^{5} - 4 q^{6} - 140 q^{9} + O(q^{10}) \) \( 3360 q - 140 q^{4} + 4 q^{5} - 4 q^{6} - 140 q^{9} + 4 q^{10} - 30 q^{11} + 2 q^{15} + 140 q^{16} + 50 q^{17} - 24 q^{19} + 10 q^{20} - 12 q^{21} + 20 q^{23} - 16 q^{24} + 48 q^{26} + 60 q^{27} - 10 q^{28} + 12 q^{30} + 12 q^{31} + 100 q^{33} + 8 q^{34} - 6 q^{35} + 140 q^{36} + 40 q^{39} + 10 q^{40} + 20 q^{41} + 10 q^{42} + 8 q^{44} + 272 q^{45} + 24 q^{49} + 8 q^{50} - 24 q^{51} + 16 q^{54} + 60 q^{55} - 12 q^{59} - 52 q^{60} - 20 q^{61} - 140 q^{64} - 4 q^{65} - 48 q^{66} - 68 q^{69} - 18 q^{70} - 90 q^{71} + 80 q^{73} - 20 q^{75} + 16 q^{76} - 80 q^{77} + 32 q^{79} + 4 q^{80} + 76 q^{81} + 330 q^{83} + 108 q^{84} + 148 q^{85} + 60 q^{86} + 20 q^{88} + 174 q^{89} + 216 q^{90} + 8 q^{91} + 48 q^{94} + 64 q^{95} - 4 q^{96} - 20 q^{97} + 40 q^{98} + 40 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2450, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2450, [\chi])\) into lower level spaces

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