Space of modular forms of level 1344, weight 4, and Character 1344.ca

• Label: 1344.4.ca
• Level: $1344$
• Weight: $4$
• Character orbit: 1344.ca
• Rep. character: $\chi_{1344}(271,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $384$
• Sturm bound: $1024$

Defining parameters

Level:	\( N \)	\(=\)	\( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1344.ca (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 112 \)
Character field:			\(\Q(\zeta_{12})\)
Sturm bound:			\(1024\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1344, [\chi])\).

	Total	New	Old
Modular forms	3136	384	2752
Cusp forms	3008	384	2624
Eisenstein series	128	0	128

Trace form

\( 384 q + 40 q^{11} - 656 q^{23} - 800 q^{29} - 456 q^{35} + 16 q^{37} + 1616 q^{43} - 752 q^{53} - 4128 q^{59} - 2256 q^{67} + 896 q^{71} + 15552 q^{81} + 3496 q^{91} + 720 q^{99}+O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(1344, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1344, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1344, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(448, [\chi])\)\(^{\oplus 2}\)