Properties

Label 1850.2.bl
Level $1850$
Weight $2$
Character orbit 1850.bl
Rep. character $\chi_{1850}(11,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $752$
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.bl (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 925 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(570\)

Dimensions

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

Total New Old
Modular forms 2320 752 1568
Cusp forms 2256 752 1504
Eisenstein series 64 0 64

Trace form

\( 752 q + 4 q^{3} - 94 q^{4} + 86 q^{9} + O(q^{10}) \) \( 752 q + 4 q^{3} - 94 q^{4} + 86 q^{9} - 4 q^{10} - 8 q^{11} + 6 q^{12} + 94 q^{16} + 8 q^{21} - 42 q^{25} - 80 q^{26} + 28 q^{27} + 28 q^{30} + 4 q^{33} - 8 q^{34} - 24 q^{35} + 172 q^{36} + 46 q^{37} - 16 q^{38} - 2 q^{40} + 30 q^{41} - 84 q^{42} - 4 q^{44} + 4 q^{46} + 8 q^{47} + 12 q^{48} - 344 q^{49} - 32 q^{53} + 114 q^{55} - 168 q^{57} + 4 q^{58} + 54 q^{59} + 72 q^{61} - 10 q^{62} + 188 q^{64} + 6 q^{65} + 26 q^{67} - 90 q^{69} + 4 q^{70} + 24 q^{71} + 8 q^{73} - 8 q^{74} + 256 q^{75} - 44 q^{77} + 30 q^{78} + 108 q^{81} + 40 q^{83} + 16 q^{84} + 112 q^{85} - 20 q^{86} + 6 q^{87} - 42 q^{89} - 4 q^{90} + 36 q^{91} + 18 q^{92} + 36 q^{93} + 12 q^{95} + 24 q^{98} - 152 q^{99} + O(q^{100}) \)

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

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