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Properties

Label 144.12.s
Level $144$
Weight $12$
Character orbit 144.s
Rep. character $\chi_{144}(47,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $132$
Sturm bound $288$

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Defining parameters

Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 144.s (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 36 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(288\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(144, [\chi])\).

Total New Old
Modular forms 540 132 408
Cusp forms 516 132 384
Eisenstein series 24 0 24

Trace form

\( 132 q + 310866 q^{9} + O(q^{10}) \) \( 132 q + 310866 q^{9} - 37698132 q^{21} + 644531250 q^{25} + 868412196 q^{29} + 111963834 q^{33} + 1431168138 q^{41} - 6711891228 q^{45} + 18643366434 q^{49} - 19132884294 q^{57} + 44593379352 q^{65} - 35251220232 q^{69} + 20795193108 q^{73} + 159081786936 q^{77} - 242646918030 q^{81} - 401476771584 q^{93} + 163385437626 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{12}^{\mathrm{new}}(144, [\chi])\) into newform subspaces

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

Decomposition of \(S_{12}^{\mathrm{old}}(144, [\chi])\) into lower level spaces

\( S_{12}^{\mathrm{old}}(144, [\chi]) \simeq \) \(S_{12}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 2}\)