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Properties

Label 1224.2.bm
Level $1224$
Weight $2$
Character orbit 1224.bm
Rep. character $\chi_{1224}(169,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $108$
Sturm bound $432$

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Defining parameters

Level: \( N \) \(=\) \( 1224 = 2^{3} \cdot 3^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1224.bm (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 153 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(432\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1224, [\chi])\).

Total New Old
Modular forms 448 108 340
Cusp forms 416 108 308
Eisenstein series 32 0 32

Trace form

\( 108 q - 6 q^{9} + 6 q^{17} - 12 q^{19} - 8 q^{21} + 54 q^{25} - 14 q^{33} + 72 q^{35} - 6 q^{43} + 12 q^{47} + 54 q^{49} - 33 q^{51} + 16 q^{53} + 22 q^{59} + 6 q^{67} + 12 q^{69} - 28 q^{77} - 18 q^{81}+ \cdots + 76 q^{93}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(1224, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1224, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1224, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(153, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(306, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(612, [\chi])\)\(^{\oplus 2}\)