Properties

Label 1840.2.ca
Level $1840$
Weight $2$
Character orbit 1840.ca
Rep. character $\chi_{1840}(49,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $700$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 1840 = 2^{4} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1840.ca (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 115 \)
Character field: \(\Q(\zeta_{22})\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1840, [\chi])\).

Total New Old
Modular forms 3000 740 2260
Cusp forms 2760 700 2060
Eisenstein series 240 40 200

Trace form

\( 700q - 9q^{5} + 48q^{9} + O(q^{10}) \) \( 700q - 9q^{5} + 48q^{9} + 6q^{11} + 27q^{15} + 38q^{19} - 38q^{21} - 9q^{25} - 10q^{29} + 10q^{31} + 7q^{35} + 30q^{39} - 26q^{41} - 16q^{45} + 48q^{49} - 2q^{51} + 11q^{55} + 18q^{59} - 2q^{61} - 35q^{65} - 30q^{69} + 18q^{71} - 39q^{75} + 6q^{79} - 220q^{81} - 3q^{85} - 18q^{89} + 308q^{91} - 89q^{95} + 30q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1840, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1840, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1840, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(230, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(460, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(920, [\chi])\)\(^{\oplus 2}\)