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Properties

Label 2450.2.be
Level $2450$
Weight $2$
Character orbit 2450.be
Rep. character $\chi_{2450}(149,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $1008$
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.be (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 245 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(840\)

Dimensions

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

Total New Old
Modular forms 5184 1008 4176
Cusp forms 4896 1008 3888
Eisenstein series 288 0 288

Trace form

\( 1008 q - 84 q^{4} + 12 q^{6} - 116 q^{9} + O(q^{10}) \) \( 1008 q - 84 q^{4} + 12 q^{6} - 116 q^{9} - 28 q^{11} - 4 q^{14} + 84 q^{16} + 24 q^{19} + 20 q^{21} - 8 q^{24} + 44 q^{26} - 4 q^{29} + 12 q^{31} + 16 q^{34} - 148 q^{36} - 32 q^{39} - 104 q^{41} + 56 q^{44} - 152 q^{46} + 176 q^{49} - 220 q^{51} + 148 q^{54} - 52 q^{56} + 80 q^{59} + 40 q^{61} + 168 q^{64} - 76 q^{71} - 32 q^{74} - 8 q^{76} + 4 q^{79} + 96 q^{81} + 88 q^{84} - 92 q^{86} + 124 q^{89} + 144 q^{91} - 136 q^{94} + 8 q^{96} - 384 q^{99} + O(q^{100}) \)

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

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