Space of modular forms of level 364, weight 2, and Character 364.bb

• Label: 364.2.bb
• Level: $364$
• Weight: $2$
• Character orbit: 364.bb
• Rep. character: $\chi_{364}(205,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $18$
• Newform subspaces: $1$
• Sturm bound: $112$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 364 = 2^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	364.bb (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 91 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(112\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(364, [\chi])\).

	Total	New	Old
Modular forms	124	18	106
Cusp forms	100	18	82
Eisenstein series	24	0	24

Trace form

18 * q + q^3 + 2 * q^7 - 6 * q^9 - 6 * q^11 - 4 * q^13 + 6 * q^15 + 20 * q^17 + 21 * q^19 + 7 * q^21 + 12 * q^23 + 5 * q^25 - 20 * q^27 + 2 * q^29 - 9 * q^31 + 12 * q^33 - 6 * q^35 + 14 * q^39 - 9 * q^41 - 14 * q^43 - 36 * q^47 + 4 * q^49 + 2 * q^51 - 13 * q^53 - q^55 + 21 * q^61 - q^63 - 12 * q^65 + 15 * q^67 - q^69 - 45 * q^71 + 33 * q^73 - 50 * q^75 - 9 * q^77 - 14 * q^79 - q^81 - 30 * q^85 - 4 * q^87 - 46 * q^91 - 60 * q^95 - 18 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(364, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
364.2.bb.a	$364$	$2$	364.bb	91.k	$6$	$18$	$9$	$2.907$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None		✓	✓	✓	364.2.bb.a	$2$	$0$	\(0\)	\(1\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{3}-\beta _{11}q^{5}+(-\beta _{7}-\beta _{13})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(364, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(364, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 2}\)