Space of modular forms of level 608, weight 3, and Character 608.bj

• Label: 608.3.bj
• Level: $608$
• Weight: $3$
• Character orbit: 608.bj
• Rep. character: $\chi_{608}(63,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $240$
• Sturm bound: $240$

Defining parameters

Level:	\( N \)	\(=\)	\( 608 = 2^{5} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	608.bj (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 76 \)
Character field:			\(\Q(\zeta_{18})\)
Sturm bound:			\(240\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(608, [\chi])\).

	Total	New	Old
Modular forms	1008	240	768
Cusp forms	912	240	672
Eisenstein series	96	0	96

Trace form

\( 240 q + 24 q^{9} + 48 q^{13} - 144 q^{21} + 120 q^{33} + 264 q^{41} + 840 q^{49} - 48 q^{53} + 816 q^{61} - 240 q^{65} - 384 q^{73} - 288 q^{77} + 936 q^{81} - 96 q^{85} + 720 q^{89} - 864 q^{93} + 216 q^{97}+O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(608, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(608, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(608, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(304, [\chi])\)\(^{\oplus 2}\)