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Properties

Label 1792.2.bd
Level $1792$
Weight $2$
Character orbit 1792.bd
Rep. character $\chi_{1792}(111,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $496$
Sturm bound $512$

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Defining parameters

Level: \( N \) \(=\) \( 1792 = 2^{8} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1792.bd (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 448 \)
Character field: \(\Q(\zeta_{16})\)
Sturm bound: \(512\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1792, [\chi])\).

Total New Old
Modular forms 2112 528 1584
Cusp forms 1984 496 1488
Eisenstein series 128 32 96

Trace form

\( 496 q + 8 q^{7} - 16 q^{9} + O(q^{10}) \) \( 496 q + 8 q^{7} - 16 q^{9} + 16 q^{11} + 16 q^{15} - 8 q^{21} + 16 q^{23} - 16 q^{25} - 16 q^{29} + 8 q^{35} - 16 q^{37} + 16 q^{39} + 16 q^{43} - 8 q^{49} + 16 q^{51} - 16 q^{53} - 16 q^{57} - 32 q^{65} - 64 q^{67} + 144 q^{71} - 8 q^{77} + 16 q^{79} - 16 q^{81} - 16 q^{85} + 8 q^{91} + 32 q^{93} + 32 q^{95} + 64 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1792, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1792, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1792, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(448, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(896, [\chi])\)\(^{\oplus 2}\)