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Properties

Label 2912.2.r
Level $2912$
Weight $2$
Character orbit 2912.r
Rep. character $\chi_{2912}(417,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $192$
Sturm bound $896$

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Defining parameters

Level: \( N \) \(=\) \( 2912 = 2^{5} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2912.r (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(896\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2912, [\chi])\).

Total New Old
Modular forms 928 192 736
Cusp forms 864 192 672
Eisenstein series 64 0 64

Trace form

\( 192 q - 96 q^{9} + O(q^{10}) \) \( 192 q - 96 q^{9} - 16 q^{21} - 80 q^{25} - 32 q^{29} + 16 q^{33} + 16 q^{45} - 16 q^{49} + 8 q^{53} + 8 q^{61} + 64 q^{69} - 32 q^{73} + 40 q^{77} - 144 q^{81} + 160 q^{85} - 48 q^{89} - 32 q^{93} + 96 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2912, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2912, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2912, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(364, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(728, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1456, [\chi])\)\(^{\oplus 2}\)