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Properties

Label 1850.2.bk
Level $1850$
Weight $2$
Character orbit 1850.bk
Rep. character $\chi_{1850}(159,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $768$
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.bk (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 2304 768 1536
Cusp forms 2240 768 1472
Eisenstein series 64 0 64

Trace form

\( 768 q + 96 q^{4} + 3 q^{5} - 104 q^{9} + O(q^{10}) \) \( 768 q + 96 q^{4} + 3 q^{5} - 104 q^{9} + 6 q^{10} + 8 q^{11} - 10 q^{12} + 12 q^{15} + 96 q^{16} + 12 q^{20} - 8 q^{21} - 47 q^{25} + 120 q^{26} + 60 q^{27} + 28 q^{30} - 23 q^{34} - 48 q^{35} + 208 q^{36} - 15 q^{37} - 3 q^{40} - 40 q^{41} - 4 q^{44} - 4 q^{46} + 40 q^{47} - 20 q^{48} + 416 q^{49} - 3 q^{50} - 50 q^{53} - 30 q^{55} + 54 q^{59} - 102 q^{61} - 30 q^{62} - 192 q^{64} - q^{65} + 10 q^{67} + 90 q^{69} - 12 q^{70} + 16 q^{71} - 28 q^{74} + 304 q^{75} - 200 q^{77} + 50 q^{78} + 42 q^{81} + 16 q^{84} - 50 q^{85} + 20 q^{86} + 150 q^{87} + 33 q^{89} - 19 q^{90} - 36 q^{91} + 30 q^{92} + 4 q^{95} - 112 q^{99} + O(q^{100}) \)

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

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