Space of modular forms of level 182, weight 4, and Character 182.g

• Label: 182.4.g
• Level: $182$
• Weight: $4$
• Character orbit: 182.g
• Rep. character: $\chi_{182}(29,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $44$
• Newform subspaces: $4$
• Sturm bound: $112$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 182 = 2 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	182.g (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(112\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(182, [\chi])\).

	Total	New	Old
Modular forms	176	44	132
Cusp forms	160	44	116
Eisenstein series	16	0	16

Trace form

44 * q + 4 * q^2 - 88 * q^4 + 20 * q^5 - 32 * q^8 - 202 * q^9 + 4 * q^10 + 24 * q^11 + 214 * q^13 + 112 * q^14 - 80 * q^15 - 352 * q^16 - 66 * q^17 - 376 * q^18 + 96 * q^19 - 40 * q^20 + 224 * q^21 - 88 * q^22 - 168 * q^23 + 2224 * q^25 - 76 * q^26 - 624 * q^27 - 338 * q^29 - 64 * q^30 - 112 * q^31 + 64 * q^32 - 84 * q^33 + 1256 * q^34 - 84 * q^35 - 808 * q^36 + 58 * q^37 + 160 * q^38 + 1792 * q^39 - 32 * q^40 + 978 * q^41 - 168 * q^42 - 488 * q^43 - 192 * q^44 + 246 * q^45 - 24 * q^46 - 2232 * q^47 - 1078 * q^49 + 24 * q^50 - 2192 * q^51 - 752 * q^52 - 2164 * q^53 - 1752 * q^54 + 2328 * q^55 - 224 * q^56 + 768 * q^57 - 964 * q^58 - 892 * q^59 + 640 * q^60 - 194 * q^61 + 312 * q^62 - 532 * q^63 + 2816 * q^64 + 290 * q^65 + 3232 * q^66 + 1620 * q^67 - 264 * q^68 - 468 * q^69 - 1352 * q^71 + 752 * q^72 + 1372 * q^73 - 2724 * q^74 + 500 * q^75 + 384 * q^76 + 784 * q^77 - 4216 * q^78 + 584 * q^79 - 160 * q^80 - 58 * q^81 + 556 * q^82 + 9728 * q^83 - 448 * q^84 + 1282 * q^85 + 560 * q^86 + 4136 * q^87 - 352 * q^88 - 2084 * q^89 - 856 * q^90 - 1344 * q^91 + 1344 * q^92 - 364 * q^93 - 1536 * q^94 - 968 * q^95 + 1496 * q^97 + 196 * q^98 - 10464 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(182, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
182.4.g.a	$182$	$4$	182.g	13.c	$3$	$8$	$4$	$10.738$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		✓			182.4.g.a	$2$	$0$	\(-8\)	\(7\)	\(-2\)	\(28\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\beta _{2}q^{2}+(-\beta _{1}-2\beta _{2})q^{3}+(-4+\cdots)q^{4}+\cdots\)
182.4.g.b	$182$	$4$	182.g	13.c	$3$	$10$	$5$	$10.738$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		✓			182.4.g.b	$2$	$0$	\(10\)	\(-1\)	\(12\)	\(-35\)	$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\beta _{4}q^{2}-\beta _{1}q^{3}+(-4+4\beta _{4})q^{4}+\cdots\)
182.4.g.c	$182$	$4$	182.g	13.c	$3$	$12$	$6$	$10.738$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			182.4.g.c	$2$	$0$	\(-12\)	\(-7\)	\(10\)	\(-42\)	$2^{2}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2-2\beta _{2})q^{2}+(-1-\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
182.4.g.d	$182$	$4$	182.g	13.c	$3$	$14$	$7$	$10.738$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		✓	✓		182.4.g.d	$2$	$0$	\(14\)	\(1\)	\(0\)	\(49\)	$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{3}]$	\(q-2\beta _{4}q^{2}+\beta _{1}q^{3}+(-4-4\beta _{4})q^{4}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(182, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(182, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 2}\)