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Properties

Label 1856.2.bg
Level $1856$
Weight $2$
Character orbit 1856.bg
Rep. character $\chi_{1856}(129,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $348$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 1856 = 2^{6} \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1856.bg (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 29 \)
Character field: \(\Q(\zeta_{14})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1856, [\chi])\).

Total New Old
Modular forms 1512 372 1140
Cusp forms 1368 348 1020
Eisenstein series 144 24 120

Trace form

\( 348 q + 10 q^{5} + 44 q^{9} + O(q^{10}) \) \( 348 q + 10 q^{5} + 44 q^{9} + 10 q^{13} + 14 q^{21} - 68 q^{25} + 20 q^{29} - 22 q^{33} + 14 q^{37} + 2 q^{45} - 56 q^{49} - 6 q^{53} - 36 q^{57} + 14 q^{61} - 18 q^{65} + 14 q^{69} + 14 q^{73} + 14 q^{77} - 96 q^{81} - 56 q^{85} - 14 q^{89} - 98 q^{93} + 14 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1856, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1856, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1856, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(29, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(58, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(116, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(232, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(464, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(928, [\chi])\)\(^{\oplus 2}\)