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

• Label: 306.2.j
• Level: $306$
• Weight: $2$
• Character orbit: 306.j
• Rep. character: $\chi_{306}(67,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $36$
• Newform subspaces: $3$
• Sturm bound: $108$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 306 = 2 \cdot 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	306.j (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 153 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(108\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	116	36	80
Cusp forms	100	36	64
Eisenstein series	16	0	16

Trace form

36 * q + 2 * q^2 - 18 * q^4 - 4 * q^8 - 18 * q^9 - 20 * q^15 - 18 * q^16 + 14 * q^17 - 8 * q^18 + 12 * q^19 + 52 * q^21 + 18 * q^25 - 16 * q^26 - 24 * q^30 + 2 * q^32 + 14 * q^33 + 3 * q^34 - 56 * q^35 + 6 * q^36 - 10 * q^38 + 4 * q^42 + 6 * q^43 + 8 * q^47 + 18 * q^49 - 14 * q^50 - 13 * q^51 - 48 * q^53 - 6 * q^59 + 16 * q^60 + 36 * q^64 + 4 * q^66 - 6 * q^67 - 7 * q^68 + 80 * q^69 - 2 * q^72 - 6 * q^76 + 24 * q^77 + 74 * q^81 + 56 * q^83 - 20 * q^84 - 24 * q^85 - 18 * q^86 - 64 * q^87 + 16 * q^89 - 100 * q^93 + 100 * 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.j.a	$306$	$2$	306.j	153.h	$6$	$4$	$2$	$2.443$	\(\Q(\zeta_{12})\)	None		✓			306.2.j.a	$4$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\zeta_{12}^{2})q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{3}+\cdots\)
306.2.j.b	$306$	$2$	306.j	153.h	$6$	$16$	$8$	$2.443$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓			306.2.j.b	$4$	$0$	\(-8\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{5}q^{2}-\beta _{1}q^{3}+(-1+\beta _{5})q^{4}+(-\beta _{6}+\cdots)q^{5}+\cdots\)
306.2.j.c	$306$	$2$	306.j	153.h	$6$	$16$	$8$	$2.443$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓			306.2.j.c	$4$	$0$	\(8\)	\(0\)	\(0\)	\(0\)	$3^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{1}q^{2}+\beta _{10}q^{3}+(-1-\beta _{1})q^{4}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(306, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(153, [\chi])\)\(^{\oplus 2}\)