Space of modular forms of level 308, weight 2, and Character 308.n

• Label: 308.2.n
• Level: $308$
• Weight: $2$
• Character orbit: 308.n
• Rep. character: $\chi_{308}(219,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $88$
• Newform subspaces: $3$
• Sturm bound: $96$
• Trace bound: $2$

Defining parameters

Level:	$N$	$=$	$308 = 2^{2} \cdot 7 \cdot 11$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	308.n (of order $6$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$308$
Character field:			$\Q(\zeta_{6})$
Newform subspaces:			$3$
Sturm bound:			$96$
Trace bound:			$2$
Distinguishing $T_p$:			$3$, $43$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(308, [\chi])$.

	Total	New	Old
Modular forms	104	104	0
Cusp forms	88	88	0
Eisenstein series	16	16	0

Trace form

88 * q - 4 * q^5 + 32 * q^9 - 14 * q^12 - 8 * q^14 + 4 * q^16 - 40 * q^25 + 10 * q^26 - 18 * q^33 - 56 * q^34 - 4 * q^36 - 20 * q^37 + 16 * q^38 - 84 * q^42 + 8 * q^44 + 48 * q^45 + 64 * q^48 - 28 * q^53 - 78 * q^56 + 6 * q^58 + 72 * q^60 - 84 * q^64 - 48 * q^66 - 72 * q^69 - 14 * q^70 + 42 * q^77 - 32 * q^78 + 62 * q^80 - 4 * q^81 + 26 * q^82 + 42 * q^86 - 52 * q^88 - 20 * q^89 - 60 * q^92 - 28 * q^93 - 96 * q^97

Decomposition of $S_{2}^{\mathrm{new}}(308, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
308.2.n.a	$308$	$2$	308.n	308.n	$6$	$4$	$2$	$2.459$	$\Q(\sqrt{-3}, \sqrt{-7})$	None		✓			308.2.n.a	$4$	$0$	$-1$	$0$	$0$	$-2$	$1$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{3}q^{2}+(1-2\beta _{1}-\beta _{2})q^{3}+(1+\beta _{1}+\cdots)q^{4}+\cdots$
308.2.n.b	$308$	$2$	308.n	308.n	$6$	$4$	$2$	$2.459$	$\Q(\sqrt{-3}, \sqrt{-7})$	None		✓			308.2.n.a	$4$	$0$	$1$	$0$	$0$	$2$	$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{3}q^{2}+(1-2\beta _{1}-\beta _{2})q^{3}+(1+\beta _{1}+\cdots)q^{4}+\cdots$
308.2.n.c	$308$	$2$	308.n	308.n	$6$	$80$	$40$	$2.459$		None		✓	✓		308.2.n.c	$8$	$0$	$0$	$0$	$-4$	$0$		$\mathrm{SU}(2)[C_{6}]$