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

• Label: 182.2.g
• Level: $182$
• Weight: $2$
• Character orbit: 182.g
• Rep. character: $\chi_{182}(29,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $12$
• Newform subspaces: $5$
• Sturm bound: $56$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 182 = 2 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	182.g (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(56\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\), \(5\)

Dimensions

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

	Total	New	Old
Modular forms	64	12	52
Cusp forms	48	12	36
Eisenstein series	16	0	16

Trace form

12 * q + 2 * q^2 - 6 * q^4 + 4 * q^5 - 4 * q^8 - 6 * q^9 - 6 * q^10 + 4 * q^11 - 6 * q^13 - 8 * q^14 - 4 * q^15 - 6 * q^16 - 6 * q^17 - 12 * q^18 + 16 * q^19 - 2 * q^20 + 8 * q^21 + 4 * q^22 - 8 * q^23 + 24 * q^25 + 10 * q^26 + 24 * q^27 - 6 * q^29 - 8 * q^30 + 8 * q^31 + 2 * q^32 - 32 * q^33 - 12 * q^34 + 8 * q^35 - 6 * q^36 - 6 * q^37 + 32 * q^38 + 12 * q^40 - 14 * q^41 + 4 * q^42 - 4 * q^43 - 8 * q^44 + 26 * q^45 - 12 * q^46 - 16 * q^47 - 6 * q^49 + 4 * q^50 + 56 * q^51 - 20 * q^53 + 12 * q^54 - 12 * q^55 + 4 * q^56 - 24 * q^57 - 2 * q^58 - 16 * q^59 + 8 * q^60 - 18 * q^61 - 12 * q^62 - 4 * q^63 + 12 * q^64 - 18 * q^65 - 16 * q^66 - 12 * q^67 - 6 * q^68 + 4 * q^69 + 6 * q^72 - 36 * q^73 + 30 * q^74 - 40 * q^75 + 16 * q^76 + 12 * q^78 + 40 * q^79 - 2 * q^80 + 30 * q^81 - 10 * q^82 - 24 * q^83 - 4 * q^84 - 34 * q^85 + 24 * q^86 + 20 * q^87 + 4 * q^88 + 28 * q^89 + 52 * q^90 + 4 * q^91 + 16 * q^92 - 40 * q^93 + 4 * q^95 + 12 * q^97 + 2 * q^98 + 40 * q^99

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.g.a	$182$	$2$	182.g	13.c	$3$	$2$	$1$	$1.453$	\(\Q(\sqrt{-3}) \)	None		✓			182.2.g.a	$2$	$0$	\(1\)	\(-3\)	\(-6\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}+(-3+3\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
182.2.g.b	$182$	$2$	182.g	13.c	$3$	$2$	$1$	$1.453$	\(\Q(\sqrt{-3}) \)	None		✓			182.2.g.b	$2$	$0$	\(1\)	\(-1\)	\(6\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
182.2.g.c	$182$	$2$	182.g	13.c	$3$	$2$	$1$	$1.453$	\(\Q(\sqrt{-3}) \)	None		✓			182.2.g.c	$2$	$0$	\(1\)	\(2\)	\(-6\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}+(2-2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
182.2.g.d	$182$	$2$	182.g	13.c	$3$	$2$	$1$	$1.453$	\(\Q(\sqrt{-3}) \)	None		✓			182.2.g.d	$2$	$0$	\(1\)	\(2\)	\(2\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}+(2-2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
182.2.g.e	$182$	$2$	182.g	13.c	$3$	$4$	$2$	$1.453$	\(\Q(\zeta_{12})\)	None		✓	✓		182.2.g.e	$2$	$0$	\(-2\)	\(0\)	\(8\)	\(2\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta_1 q^{2}+\beta_{2} q^{3}+(\beta_1-1)q^{4}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(182, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 2}\)