Properties

Label 1840.2.bo
Level $1840$
Weight $2$
Character orbit 1840.bo
Rep. character $\chi_{1840}(81,\cdot)$
Character field $\Q(\zeta_{11})$
Dimension $480$
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.bo (of order \(11\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 23 \)
Character field: \(\Q(\zeta_{11})\)
Sturm bound: \(576\)

Dimensions

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

Total New Old
Modular forms 3000 480 2520
Cusp forms 2760 480 2280
Eisenstein series 240 0 240

Trace form

\( 480q + 4q^{7} - 48q^{9} + O(q^{10}) \) \( 480q + 4q^{7} - 48q^{9} + 8q^{11} + 4q^{15} + 8q^{19} + 8q^{21} + 4q^{23} - 48q^{25} + 12q^{27} - 8q^{29} + 8q^{31} - 16q^{37} + 12q^{39} + 8q^{41} - 4q^{43} + 8q^{45} - 24q^{47} - 40q^{49} + 8q^{51} - 16q^{53} - 12q^{59} - 16q^{61} + 20q^{63} + 8q^{65} + 28q^{67} + 12q^{69} - 16q^{71} + 104q^{77} + 156q^{79} - 56q^{81} + 72q^{83} - 16q^{85} + 336q^{87} - 72q^{89} + 272q^{93} - 72q^{97} + 364q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1840, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(46, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(92, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(184, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(230, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(368, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(460, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(920, [\chi])\)\(^{\oplus 2}\)