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Properties

Label 1840.4.ca
Level $1840$
Weight $4$
Character orbit 1840.ca
Rep. character $\chi_{1840}(49,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $2140$
Sturm bound $1152$

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Defining parameters

Level: \( N \) \(=\) \( 1840 = 2^{4} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1840.ca (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 115 \)
Character field: \(\Q(\zeta_{22})\)
Sturm bound: \(1152\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1840, [\chi])\).

Total New Old
Modular forms 8760 2180 6580
Cusp forms 8520 2140 6380
Eisenstein series 240 40 200

Trace form

\( 2140 q - 9 q^{5} + 1872 q^{9} + O(q^{10}) \) \( 2140 q - 9 q^{5} + 1872 q^{9} + 150 q^{11} + 75 q^{15} - 234 q^{19} + 10 q^{21} - 9 q^{25} + 38 q^{29} - 246 q^{31} - 89 q^{35} + 126 q^{39} + 278 q^{41} + 176 q^{45} + 9776 q^{49} + 606 q^{51} - 2245 q^{55} + 18 q^{59} - 930 q^{61} + 205 q^{65} + 698 q^{69} + 18 q^{71} - 9711 q^{75} + 3014 q^{79} - 19516 q^{81} - 1555 q^{85} + 1262 q^{89} - 20428 q^{91} + 7671 q^{95} - 6354 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1840, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1840, [\chi])\) into lower level spaces

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