Space of modular forms of level 1344, weight 2, and Character 1344.bj

• Label: 1344.2.bj
• Level: $1344$
• Weight: $2$
• Character orbit: 1344.bj
• Rep. character: $\chi_{1344}(191,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $120$
• Sturm bound: $512$

Defining parameters

Level:	\( N \)	\(=\)	\( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1344.bj (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 84 \)
Character field:			\(\Q(\zeta_{6})\)
Sturm bound:			\(512\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1344, [\chi])\).

	Total	New	Old
Modular forms	560	136	424
Cusp forms	464	120	344
Eisenstein series	96	16	80

Trace form

\( 120 q - 2 q^{9} + 10 q^{21} + 40 q^{25} + 10 q^{33} - 4 q^{37} + 22 q^{45} - 8 q^{49} - 20 q^{57} + 20 q^{61} - 4 q^{69} - 4 q^{73} - 18 q^{81} + 56 q^{85} + 14 q^{93} - 48 q^{97}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1344, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1344, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1344, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(672, [\chi])\)\(^{\oplus 2}\)