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

• Label: 182.2.m
• Level: $182$
• Weight: $2$
• Character orbit: 182.m
• Rep. character: $\chi_{182}(43,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $16$
• Newform subspaces: $2$
• Sturm bound: $56$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 182 = 2 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	182.m (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(56\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	64	16	48
Cusp forms	48	16	32
Eisenstein series	16	0	16

Trace form

16 * q + 8 * q^4 - 8 * q^9 - 4 * q^10 - 12 * q^11 - 8 * q^13 + 8 * q^14 - 12 * q^15 - 8 * q^16 - 4 * q^17 - 4 * q^22 - 8 * q^25 + 24 * q^27 - 4 * q^29 + 16 * q^30 + 24 * q^33 + 8 * q^36 + 12 * q^37 + 16 * q^38 - 48 * q^39 - 8 * q^40 - 36 * q^41 - 4 * q^42 + 12 * q^43 + 60 * q^45 - 12 * q^46 + 8 * q^49 - 12 * q^50 - 40 * q^51 - 4 * q^52 + 56 * q^53 - 36 * q^54 - 4 * q^55 + 4 * q^56 + 24 * q^58 - 8 * q^61 + 12 * q^62 - 12 * q^63 - 16 * q^64 - 24 * q^65 - 16 * q^66 - 12 * q^67 + 4 * q^68 + 20 * q^69 - 12 * q^72 - 40 * q^75 - 4 * q^78 + 8 * q^79 - 36 * q^81 + 8 * q^82 + 12 * q^84 + 60 * q^85 - 4 * q^87 + 4 * q^88 + 16 * q^90 - 20 * q^91 + 48 * q^93 + 16 * q^94 + 36 * q^95 + 48 * q^97

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.m.a	$182$	$2$	182.m	13.e	$6$	$4$	$2$	$1.453$	\(\Q(\zeta_{12})\)	None		✓			182.2.m.a	$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+(1-\zeta_{12}-\zeta_{12}^{2}+2\zeta_{12}^{3})q^{3}+\cdots\)
182.2.m.b	$182$	$2$	182.m	13.e	$6$	$12$	$6$	$1.453$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓	✓		182.2.m.b	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{5}q^{2}+(\beta _{2}+\beta _{10})q^{3}+(1-\beta _{7})q^{4}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(182, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 2}\)