Space of modular forms of level 608, weight 2, and Character 608.bm

• Label: 608.2.bm
• Level: $608$
• Weight: $2$
• Character orbit: 608.bm
• Rep. character: $\chi_{608}(45,\cdot)$
• Character field: $\Q(\zeta_{24})$
• Dimension: $624$
• Newform subspaces: $1$
• Sturm bound: $160$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 608 = 2^{5} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	608.bm (of order \(24\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 608 \)
Character field:			\(\Q(\zeta_{24})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(160\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(608, [\chi])\).

	Total	New	Old
Modular forms	656	656	0
Cusp forms	624	624	0
Eisenstein series	32	32	0

Trace form

624 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 16 * q^7 - 16 * q^8 - 4 * q^9 + 4 * q^10 - 16 * q^11 - 16 * q^12 - 4 * q^13 - 4 * q^14 - 4 * q^16 - 16 * q^18 - 8 * q^19 - 16 * q^20 - 4 * q^21 - 4 * q^22 - 4 * q^23 - 20 * q^24 - 4 * q^25 + 24 * q^26 - 16 * q^27 + 36 * q^28 - 4 * q^29 - 32 * q^30 + 64 * q^31 + 36 * q^32 - 8 * q^33 - 40 * q^34 - 52 * q^35 - 4 * q^36 - 16 * q^37 - 76 * q^38 - 16 * q^39 - 24 * q^40 - 4 * q^41 + 36 * q^42 - 4 * q^43 + 40 * q^44 - 40 * q^45 - 80 * q^46 - 4 * q^48 - 64 * q^50 - 44 * q^51 + 28 * q^52 - 4 * q^53 + 8 * q^54 - 4 * q^55 - 96 * q^56 - 8 * q^57 - 16 * q^58 - 4 * q^59 + 88 * q^60 - 68 * q^61 + 12 * q^62 - 8 * q^63 + 56 * q^64 - 32 * q^65 + 76 * q^66 - 4 * q^67 - 152 * q^68 + 112 * q^69 - 52 * q^70 - 4 * q^71 - 4 * q^72 - 4 * q^73 - 4 * q^74 - 56 * q^75 - 8 * q^76 - 16 * q^77 - 4 * q^78 + 92 * q^80 + 36 * q^82 - 16 * q^83 - 16 * q^84 - 44 * q^85 - 68 * q^86 - 128 * q^87 + 64 * q^88 - 4 * q^89 - 124 * q^90 - 4 * q^91 - 4 * q^92 - 16 * q^93 + 176 * q^94 - 16 * q^95 - 224 * q^96 - 8 * q^97 + 144 * q^98 - 44 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(608, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
608.2.bm.a	$608$	$2$	608.bm	608.am	$24$	$624$	$78$	$4.855$		None		✓	✓	✓	608.2.bm.a	$4$	$0$	\(-4\)	\(-4\)	\(-4\)	\(-16\)		$\mathrm{SU}(2)[C_{24}]$