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Properties

Label 1450.2.r
Level $1450$
Weight $2$
Character orbit 1450.r
Rep. character $\chi_{1450}(49,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $276$
Sturm bound $450$

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Defining parameters

Level: \( N \) \(=\) \( 1450 = 2 \cdot 5^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1450.r (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 145 \)
Character field: \(\Q(\zeta_{14})\)
Sturm bound: \(450\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1450, [\chi])\).

Total New Old
Modular forms 1428 276 1152
Cusp forms 1284 276 1008
Eisenstein series 144 0 144

Trace form

\( 276 q + 46 q^{4} - 24 q^{6} + 26 q^{9} + O(q^{10}) \) \( 276 q + 46 q^{4} - 24 q^{6} + 26 q^{9} + 16 q^{11} - 8 q^{14} - 46 q^{16} + 16 q^{19} - 76 q^{21} + 24 q^{24} + 30 q^{26} + 50 q^{29} - 32 q^{31} - 58 q^{34} - 54 q^{36} + 8 q^{39} - 12 q^{41} + 40 q^{44} + 40 q^{46} + 106 q^{49} - 16 q^{51} - 4 q^{54} + 8 q^{56} - 72 q^{59} + 84 q^{61} + 46 q^{64} + 48 q^{66} + 80 q^{69} + 92 q^{71} + 128 q^{74} + 40 q^{76} + 16 q^{79} + 58 q^{81} - 92 q^{84} + 128 q^{86} - 28 q^{89} + 60 q^{94} + 4 q^{96} + 136 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1450, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1450, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1450, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(145, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(290, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(725, [\chi])\)\(^{\oplus 2}\)