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Properties

Label 2450.4.t
Level $2450$
Weight $4$
Character orbit 2450.t
Rep. character $\chi_{2450}(449,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $1512$
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.t (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 245 \)
Character field: \(\Q(\zeta_{14})\)
Sturm bound: \(1680\)

Dimensions

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

Total New Old
Modular forms 7632 1512 6120
Cusp forms 7488 1512 5976
Eisenstein series 144 0 144

Trace form

\( 1512 q + 1008 q^{4} + 64 q^{6} + 2408 q^{9} + O(q^{10}) \) \( 1512 q + 1008 q^{4} + 64 q^{6} + 2408 q^{9} + 224 q^{11} - 96 q^{14} - 4032 q^{16} + 176 q^{19} + 104 q^{21} - 32 q^{24} - 448 q^{26} + 588 q^{29} - 1048 q^{31} - 272 q^{34} - 9632 q^{36} - 1400 q^{39} + 1248 q^{41} - 112 q^{44} + 3304 q^{46} - 4404 q^{49} + 2184 q^{51} - 3080 q^{54} + 160 q^{56} + 5168 q^{59} + 1268 q^{61} + 16128 q^{64} - 32 q^{66} - 6464 q^{69} + 10808 q^{71} + 3640 q^{74} + 1424 q^{76} - 1176 q^{79} - 13776 q^{81} - 1760 q^{84} + 2744 q^{86} - 13352 q^{89} + 10456 q^{91} - 11560 q^{94} + 128 q^{96} - 30072 q^{99} + O(q^{100}) \)

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

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