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Properties

Label 1792.2.bq
Level $1792$
Weight $2$
Character orbit 1792.bq
Rep. character $\chi_{1792}(47,\cdot)$
Character field $\Q(\zeta_{48})$
Dimension $992$
Sturm bound $512$

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Defining parameters

Level: \( N \) \(=\) \( 1792 = 2^{8} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1792.bq (of order \(48\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 448 \)
Character field: \(\Q(\zeta_{48})\)
Sturm bound: \(512\)

Dimensions

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

Total New Old
Modular forms 4224 1056 3168
Cusp forms 3968 992 2976
Eisenstein series 256 64 192

Trace form

\( 992 q + 24 q^{3} - 24 q^{5} + 16 q^{7} - 8 q^{9} + O(q^{10}) \) \( 992 q + 24 q^{3} - 24 q^{5} + 16 q^{7} - 8 q^{9} + 8 q^{11} + 32 q^{15} - 24 q^{17} + 24 q^{19} - 16 q^{21} + 8 q^{23} - 8 q^{25} - 32 q^{29} + 48 q^{31} + 16 q^{35} - 8 q^{37} + 8 q^{39} + 32 q^{43} - 24 q^{45} + 24 q^{47} - 16 q^{49} + 8 q^{51} - 8 q^{53} - 32 q^{57} + 216 q^{59} - 24 q^{61} - 16 q^{65} + 88 q^{67} - 96 q^{71} - 24 q^{73} + 24 q^{75} - 16 q^{77} + 8 q^{79} - 8 q^{81} - 32 q^{85} + 24 q^{87} - 24 q^{89} + 16 q^{91} - 56 q^{93} + 16 q^{95} - 16 q^{99} + O(q^{100}) \)

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

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