Space of modular forms of level 306, weight 2, and Character 306.b

• Label: 306.2.b
• Level: $306$
• Weight: $2$
• Character orbit: 306.b
• Rep. character: $\chi_{306}(271,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $4$
• Sturm bound: $108$
• Trace bound: $17$

Defining parameters

Level:	$N$	$=$	$306 = 2 \cdot 3^{2} \cdot 17$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	306.b (of order $2$ and degree $1$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$17$
Character field:			$\Q$
Newform subspaces:			$4$
Sturm bound:			$108$
Trace bound:			$17$
Distinguishing $T_p$:			$5$, $47$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(306, [\chi])$.

	Total	New	Old
Modular forms	62	8	54
Cusp forms	46	8	38
Eisenstein series	16	0	16

Trace form

8 * q + 8 * q^4 + 8 * q^16 + 8 * q^17 + 8 * q^25 + 16 * q^26 - 8 * q^34 - 8 * q^35 - 8 * q^38 - 16 * q^43 - 16 * q^47 - 24 * q^49 - 8 * q^50 - 24 * q^59 + 8 * q^64 - 32 * q^67 + 8 * q^68 - 16 * q^70 + 56 * q^83 - 16 * q^85 - 16 * q^86 - 32 * q^89 - 32 * q^94 + 8 * q^98

Decomposition of $S_{2}^{\mathrm{new}}(306, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
306.2.b.a	$306$	$2$	306.b	17.b	$2$	$2$	$2$	$2.443$	$\Q(\sqrt{-1})$	None					102.2.b.a	$2$	$0$	$-2$	$0$	$0$	$0$	$2$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+q^{4}+\beta q^{5}+\beta q^{7}-q^{8}+\cdots$
306.2.b.b	$306$	$2$	306.b	17.b	$2$	$2$	$2$	$2.443$	$\Q(\sqrt{-2})$	None		✓			306.2.b.b	$2$	$0$	$-2$	$0$	$0$	$0$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+q^{4}+\beta q^{5}-3\beta q^{7}-q^{8}-\beta q^{10}+\cdots$
306.2.b.c	$306$	$2$	306.b	17.b	$2$	$2$	$2$	$2.443$	$\Q(\sqrt{-2})$	None		✓			306.2.b.b	$2$	$0$	$2$	$0$	$0$	$0$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+q^{4}+\beta q^{5}+3\beta q^{7}+q^{8}+\beta q^{10}+\cdots$
306.2.b.d	$306$	$2$	306.b	17.b	$2$	$2$	$2$	$2.443$	$\Q(\sqrt{-2})$	None					34.2.b.a	$2$	$0$	$2$	$0$	$0$	$0$	$2$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+q^{4}+\beta q^{5}+q^{8}+\beta q^{10}+\beta q^{11}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(306, [\chi])$ into lower level spaces

$S_{2}^{\mathrm{old}}(306, [\chi]) \simeq$ $S_{2}^{\mathrm{new}}(34, [\chi])$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(51, [\chi])$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(102, [\chi])$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(153, [\chi])$$^{\oplus 2}$