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Properties

Label 2450.2.bb
Level $2450$
Weight $2$
Character orbit 2450.bb
Rep. character $\chi_{2450}(79,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $800$
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.bb (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 175 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(840\)

Dimensions

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

Total New Old
Modular forms 3488 800 2688
Cusp forms 3232 800 2432
Eisenstein series 256 0 256

Trace form

\( 800 q - 100 q^{4} + 2 q^{5} - 8 q^{6} - 100 q^{9} + O(q^{10}) \) \( 800 q - 100 q^{4} + 2 q^{5} - 8 q^{6} - 100 q^{9} + 2 q^{10} + 6 q^{11} + 48 q^{15} + 100 q^{16} + 20 q^{17} - 4 q^{19} + 4 q^{20} - 80 q^{22} + 50 q^{23} + 16 q^{24} - 48 q^{26} + 120 q^{27} - 48 q^{29} + 46 q^{30} + 6 q^{31} + 50 q^{33} + 16 q^{34} - 200 q^{36} + 44 q^{39} - 2 q^{40} - 68 q^{41} + 4 q^{44} - 16 q^{45} - 24 q^{46} - 12 q^{51} - 100 q^{53} - 16 q^{54} - 24 q^{55} - 24 q^{59} - 6 q^{60} + 8 q^{61} + 200 q^{64} - 30 q^{65} + 116 q^{69} - 100 q^{71} + 40 q^{73} + 24 q^{74} - 196 q^{75} + 32 q^{76} + 2 q^{80} + 44 q^{81} + 160 q^{83} - 156 q^{85} - 12 q^{86} + 10 q^{88} - 54 q^{89} + 80 q^{92} + 28 q^{95} + 4 q^{96} + 20 q^{97} + 88 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2450, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1225, [\chi])\)\(^{\oplus 2}\)