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Properties

Label 1850.2.bj
Level $1850$
Weight $2$
Character orbit 1850.bj
Rep. character $\chi_{1850}(269,\cdot)$
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.bj (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

\( 752 q - 94 q^{4} + 16 q^{5} - 94 q^{9} + O(q^{10}) \) \( 752 q - 94 q^{4} + 16 q^{5} - 94 q^{9} - 4 q^{10} + 8 q^{11} - 10 q^{12} + 94 q^{16} + 4 q^{20} - 8 q^{21} - 40 q^{22} - 50 q^{25} - 112 q^{26} - 60 q^{27} - 8 q^{29} + 28 q^{30} + 48 q^{31} + 8 q^{34} - 8 q^{35} - 188 q^{36} + 10 q^{37} - 2 q^{40} - 38 q^{41} + 4 q^{44} + 96 q^{45} - 20 q^{46} - 40 q^{47} + 20 q^{48} + 344 q^{49} + 32 q^{50} - 24 q^{51} - 40 q^{53} - 58 q^{55} + 6 q^{59} - 20 q^{60} - 24 q^{61} + 30 q^{62} + 188 q^{64} + 30 q^{65} - 32 q^{66} + 10 q^{67} - 22 q^{69} - 12 q^{70} - 48 q^{71} - 8 q^{74} + 304 q^{75} - 120 q^{77} - 50 q^{78} + 8 q^{80} + 72 q^{81} - 16 q^{84} - 96 q^{85} - 20 q^{86} - 50 q^{87} + 14 q^{89} + 44 q^{90} + 12 q^{91} + 10 q^{92} - 24 q^{95} - 120 q^{97} + 56 q^{99} + O(q^{100}) \)

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

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