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Properties

Label 2450.4.be
Level $2450$
Weight $4$
Character orbit 2450.be
Rep. character $\chi_{2450}(149,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $3024$
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.be (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 245 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(1680\)

Dimensions

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

Total New Old
Modular forms 15264 3024 12240
Cusp forms 14976 3024 11952
Eisenstein series 288 0 288

Trace form

\( 3024 q - 1008 q^{4} + 8 q^{6} - 2492 q^{9} + O(q^{10}) \) \( 3024 q - 1008 q^{4} + 8 q^{6} - 2492 q^{9} - 476 q^{11} - 168 q^{14} + 4032 q^{16} - 596 q^{19} + 412 q^{21} + 128 q^{24} + 904 q^{26} - 588 q^{29} - 308 q^{31} - 544 q^{34} - 17584 q^{36} - 2464 q^{39} - 240 q^{41} - 1232 q^{44} + 6944 q^{46} - 9264 q^{49} + 8148 q^{51} - 808 q^{54} - 736 q^{56} + 4744 q^{59} + 4648 q^{61} + 32256 q^{64} - 1600 q^{66} + 104 q^{69} - 10808 q^{71} - 5824 q^{74} - 512 q^{76} - 588 q^{79} + 20496 q^{81} + 1184 q^{84} - 392 q^{86} + 26372 q^{89} - 11212 q^{91} + 16528 q^{94} - 512 q^{96} + 30072 q^{99} + O(q^{100}) \)

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

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