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Properties

Label 1856.2.j
Level $1856$
Weight $2$
Character orbit 1856.j
Rep. character $\chi_{1856}(911,\cdot)$
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.j (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

\( 116 q + 8 q^{7} - 108 q^{9} + O(q^{10}) \) \( 116 q + 8 q^{7} - 108 q^{9} + 12 q^{11} - 12 q^{15} - 4 q^{17} + 8 q^{23} - 10 q^{29} - 20 q^{37} + 28 q^{39} + 12 q^{43} - 24 q^{45} + 84 q^{49} - 12 q^{51} - 20 q^{53} + 4 q^{55} + 24 q^{57} + 4 q^{59} - 4 q^{61} - 24 q^{63} - 8 q^{65} + 40 q^{67} + 8 q^{73} - 44 q^{75} - 16 q^{77} - 40 q^{79} + 76 q^{81} + 4 q^{83} + 16 q^{85} + 4 q^{87} - 8 q^{89} - 24 q^{91} - 36 q^{93} - 20 q^{95} - 4 q^{97} - 12 q^{99} + O(q^{100}) \)

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

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