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Properties

Label 2450.2.t
Level $2450$
Weight $2$
Character orbit 2450.t
Rep. character $\chi_{2450}(449,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $504$
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.t (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 245 \)
Character field: \(\Q(\zeta_{14})\)
Sturm bound: \(840\)

Dimensions

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

Total New Old
Modular forms 2592 504 2088
Cusp forms 2448 504 1944
Eisenstein series 144 0 144

Trace form

\( 504 q + 84 q^{4} - 24 q^{6} + 104 q^{9} + O(q^{10}) \) \( 504 q + 84 q^{4} - 24 q^{6} + 104 q^{9} + 28 q^{11} - 8 q^{14} - 84 q^{16} - 24 q^{19} - 8 q^{21} - 4 q^{24} - 32 q^{26} + 4 q^{29} + 8 q^{34} - 104 q^{36} + 20 q^{39} - 64 q^{41} + 28 q^{44} - 52 q^{46} + 100 q^{49} - 104 q^{51} + 68 q^{54} - 20 q^{56} + 88 q^{59} + 56 q^{61} + 84 q^{64} - 48 q^{66} + 24 q^{69} + 76 q^{71} + 20 q^{74} - 4 q^{76} + 8 q^{79} - 144 q^{81} - 76 q^{84} + 68 q^{86} - 124 q^{89} - 144 q^{91} + 124 q^{94} + 4 q^{96} + 384 q^{99} + O(q^{100}) \)

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

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