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Properties

Label 2230.2.b
Level $2230$
Weight $2$
Character orbit 2230.b
Rep. character $\chi_{2230}(1339,\cdot)$
Character field $\Q$
Dimension $112$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 2230 = 2 \cdot 5 \cdot 223 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2230.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2230, [\chi])\).

Total New Old
Modular forms 340 112 228
Cusp forms 332 112 220
Eisenstein series 8 0 8

Trace form

\( 112 q - 112 q^{4} - 4 q^{5} - 116 q^{9} + O(q^{10}) \) \( 112 q - 112 q^{4} - 4 q^{5} - 116 q^{9} + 4 q^{10} + 8 q^{11} - 8 q^{14} + 8 q^{15} + 112 q^{16} - 4 q^{19} + 4 q^{20} - 8 q^{26} + 4 q^{29} + 20 q^{30} - 16 q^{31} + 16 q^{35} + 116 q^{36} - 48 q^{39} - 4 q^{40} + 24 q^{41} - 8 q^{44} + 16 q^{45} - 8 q^{46} - 152 q^{49} + 8 q^{50} + 16 q^{51} + 24 q^{55} + 8 q^{56} - 8 q^{59} - 8 q^{60} + 8 q^{61} - 112 q^{64} + 4 q^{65} - 56 q^{69} + 8 q^{70} + 24 q^{71} - 12 q^{74} + 16 q^{75} + 4 q^{76} - 24 q^{79} - 4 q^{80} + 192 q^{81} - 4 q^{85} - 4 q^{86} - 40 q^{89} - 4 q^{90} + 88 q^{91} - 40 q^{94} - 16 q^{95} - 88 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2230, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2230, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2230, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(1115, [\chi])\)\(^{\oplus 2}\)