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Properties

Label 1856.2.t
Level $1856$
Weight $2$
Character orbit 1856.t
Rep. character $\chi_{1856}(655,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $116$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 1856 = 2^{6} \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1856.t (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 464 \)
Character field: \(\Q(i)\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 496 124 372
Cusp forms 464 116 348
Eisenstein series 32 8 24

Trace form

\( 116 q + 4 q^{3} + 8 q^{7} + 108 q^{9} + O(q^{10}) \) \( 116 q + 4 q^{3} + 8 q^{7} + 108 q^{9} + 12 q^{15} - 4 q^{17} + 4 q^{19} - 16 q^{21} + 8 q^{23} - 8 q^{27} + 6 q^{29} + 28 q^{39} - 24 q^{45} + 84 q^{49} + 12 q^{51} - 20 q^{53} + 4 q^{55} - 24 q^{57} + 4 q^{59} + 24 q^{63} - 8 q^{65} - 40 q^{67} - 16 q^{69} - 8 q^{73} + 40 q^{79} + 76 q^{81} + 4 q^{83} + 4 q^{87} + 8 q^{89} + 24 q^{91} + 36 q^{93} + 20 q^{95} - 4 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1856, [\chi]) \cong \)