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

• Label: 182.2.d
• Level: $182$
• Weight: $2$
• Character orbit: 182.d
• Rep. character: $\chi_{182}(155,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• 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.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q\)
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	32	8	24
Cusp forms	24	8	16
Eisenstein series	8	0	8

Trace form

8 * q - 8 * q^4 + 20 * q^9 - 8 * q^10 - 16 * q^13 + 4 * q^14 + 8 * q^16 - 8 * q^17 + 4 * q^22 + 12 * q^23 - 16 * q^25 - 24 * q^27 + 16 * q^29 + 8 * q^30 - 20 * q^36 - 16 * q^38 + 8 * q^40 + 4 * q^42 + 24 * q^43 - 8 * q^49 - 8 * q^51 + 16 * q^52 - 8 * q^53 + 40 * q^55 - 4 * q^56 - 16 * q^61 + 24 * q^62 - 8 * q^64 - 12 * q^65 - 32 * q^66 + 8 * q^68 + 16 * q^69 + 12 * q^74 - 80 * q^75 - 24 * q^77 - 44 * q^78 - 44 * q^79 + 48 * q^81 + 40 * q^82 + 88 * q^87 - 4 * q^88 + 32 * q^90 + 8 * q^91 - 12 * q^92 + 8 * q^94 + 24 * q^95

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.d.a	$182$	$2$	182.d	13.b	$2$	$2$	$2$	$1.453$	\(\Q(\sqrt{-1}) \)	None		✓			182.2.d.a	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-q^{3}-q^{4}+2 i q^{5}-i q^{6}+\cdots\)
182.2.d.b	$182$	$2$	182.d	13.b	$2$	$6$	$6$	$1.453$	6.0.30647296.1	None		✓	✓		182.2.d.b	$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{2}+\beta _{3}q^{3}-q^{4}+(-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)

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

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