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Properties

Label 1850.2.br
Level $1850$
Weight $2$
Character orbit 1850.br
Rep. character $\chi_{1850}(57,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $684$
Sturm bound $570$

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Defining parameters

Level: \( N \) \(=\) \( 1850 = 2 \cdot 5^{2} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1850.br (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 185 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(570\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1850, [\chi])\).

Total New Old
Modular forms 3564 684 2880
Cusp forms 3276 684 2592
Eisenstein series 288 0 288

Trace form

\( 684 q - 12 q^{3} + O(q^{10}) \) \( 684 q - 12 q^{3} + 12 q^{12} + 48 q^{14} + 6 q^{17} + 12 q^{27} - 12 q^{33} + 24 q^{37} - 126 q^{41} - 84 q^{42} + 24 q^{44} - 144 q^{49} - 24 q^{53} + 24 q^{57} + 42 q^{58} + 36 q^{61} + 60 q^{62} + 342 q^{64} + 84 q^{67} + 336 q^{69} + 96 q^{71} - 6 q^{73} + 222 q^{74} - 24 q^{76} - 60 q^{77} - 24 q^{79} + 72 q^{81} + 96 q^{83} - 48 q^{86} + 216 q^{87} - 24 q^{88} - 24 q^{89} + 72 q^{91} + 24 q^{92} - 24 q^{97} + 24 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1850, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1850, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1850, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(185, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(370, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(925, [\chi])\)\(^{\oplus 2}\)