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Properties

Label 112.8.w
Level $112$
Weight $8$
Character orbit 112.w
Rep. character $\chi_{112}(37,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $440$
Sturm bound $128$

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Defining parameters

Level: \( N \) \(=\) \( 112 = 2^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 112.w (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 112 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(128\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(112, [\chi])\).

Total New Old
Modular forms 456 456 0
Cusp forms 440 440 0
Eisenstein series 16 16 0

Trace form

\( 440 q - 2 q^{2} - 2 q^{3} + 180 q^{4} - 2 q^{5} - 8 q^{6} + 1996 q^{8} + 6472 q^{10} - 1206 q^{11} - 2 q^{12} - 8 q^{13} + 25932 q^{14} - 16 q^{15} - 26392 q^{16} - 4 q^{17} + 71946 q^{18} - 2 q^{19} + 81992 q^{20}+ \cdots - 10345976 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{8}^{\mathrm{new}}(112, [\chi])\) into newform subspaces

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