Space of modular forms of level 182, weight 2, and Character 182.v

• Label: 182.2.v
• Level: $182$
• Weight: $2$
• Character orbit: 182.v
• Rep. character: $\chi_{182}(121,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $20$
• Newform subspaces: $1$
• Sturm bound: $56$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 182 = 2 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	182.v (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 91 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(56\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(182, [\chi])\).

	Total	New	Old
Modular forms	64	20	44
Cusp forms	48	20	28
Eisenstein series	16	0	16

Trace form

20 * q - 4 * q^3 + 10 * q^4 - 2 * q^7 + 32 * q^9 + 8 * q^10 - 2 * q^12 + 6 * q^13 - 4 * q^14 - 12 * q^15 - 10 * q^16 - 10 * q^17 - 24 * q^18 + 14 * q^21 + 2 * q^22 + 18 * q^25 - 6 * q^26 - 28 * q^27 - 4 * q^28 + 2 * q^29 + 4 * q^30 + 6 * q^31 - 36 * q^35 + 16 * q^36 - 36 * q^37 - 14 * q^38 - 26 * q^39 + 4 * q^40 + 18 * q^41 - 4 * q^42 + 8 * q^43 - 6 * q^44 - 60 * q^45 + 12 * q^46 - 18 * q^47 + 2 * q^48 - 12 * q^50 - 22 * q^51 - 4 * q^53 - 18 * q^54 + 2 * q^55 - 2 * q^56 - 12 * q^60 + 8 * q^61 - 24 * q^62 + 64 * q^63 - 20 * q^64 - 18 * q^65 + 32 * q^66 + 10 * q^68 - 34 * q^69 + 48 * q^70 - 18 * q^71 + 72 * q^73 + 12 * q^74 - 18 * q^75 + 24 * q^76 + 42 * q^77 + 20 * q^78 + 42 * q^79 + 4 * q^81 + 32 * q^82 + 16 * q^84 - 12 * q^85 - 42 * q^86 - 64 * q^87 + 4 * q^88 - 18 * q^89 + 52 * q^90 + 60 * q^91 + 60 * q^93 - 32 * q^94 - 12 * q^95 + 78 * q^97 + 12 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(182, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
182.2.v.a	$182$	$2$	182.v	91.u	$6$	$20$	$10$	$1.453$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		✓	✓	✓	182.2.o.a	$2$	$0$	\(0\)	\(-4\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{6}q^{2}-\beta _{3}q^{3}+\beta _{4}q^{4}+(-\beta _{8}+\beta _{16}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(182, [\chi])\) into lower level spaces

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