Space of modular forms of level 182, weight 6, and trivial character

• Label: 182.6.a
• Level: $182$
• Weight: $6$
• Character orbit: 182.a
• Rep. character: $\chi_{182}(1,\cdot)$
• Character field: $\Q$
• Dimension: $30$
• Newform subspaces: $10$
• Sturm bound: $168$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 182 = 2 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	182.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(168\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(182))\).

	Total	New	Old
Modular forms	144	30	114
Cusp forms	136	30	106
Eisenstein series	8	0	8

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)	\(7\)	\(13\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(3\)
\(+\)	\(+\)	\(-\)	$-$	\(4\)
\(+\)	\(-\)	\(+\)	$-$	\(4\)
\(+\)	\(-\)	\(-\)	$+$	\(3\)
\(-\)	\(+\)	\(+\)	$-$	\(5\)
\(-\)	\(+\)	\(-\)	$+$	\(3\)
\(-\)	\(-\)	\(+\)	$+$	\(3\)
\(-\)	\(-\)	\(-\)	$-$	\(5\)
Plus space			\(+\)	\(12\)
Minus space			\(-\)	\(18\)

Trace form

\( 30 q + 8 q^{2} - 36 q^{3} + 480 q^{4} - 232 q^{5} + 16 q^{6} + 128 q^{8} + 2634 q^{9} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(182))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces					A-L signs			Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	7	13
182.6.a.a	$182$	$6$	182.a	1.a	$1$	$1$	$1$	$29.190$	\(\Q\)	None	✓	$1$	$1$	\(-4\)	\(-12\)	\(51\)	\(49\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{2}-12q^{3}+2^{4}q^{4}+51q^{5}+48q^{6}+\cdots\)
182.6.a.b	$182$	$6$	182.a	1.a	$1$	$1$	$1$	$29.190$	\(\Q\)	None	✓	$1$	$1$	\(4\)	\(-30\)	\(29\)	\(-49\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+4q^{2}-30q^{3}+2^{4}q^{4}+29q^{5}-120q^{6}+\cdots\)
182.6.a.c	$182$	$6$	182.a	1.a	$1$	$2$	$2$	$29.190$	\(\Q(\sqrt{211}) \)	None	✓	$1$	$1$	\(-8\)	\(-2\)	\(-132\)	\(98\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{2}+(-1+\beta )q^{3}+2^{4}q^{4}+(-66+\cdots)q^{5}+\cdots\)
182.6.a.d	$182$	$6$	182.a	1.a	$1$	$2$	$2$	$29.190$	\(\Q(\sqrt{14}) \)	None	✓	$1$	$1$	\(8\)	\(8\)	\(-54\)	\(-98\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+4q^{2}+(4+3\beta )q^{3}+2^{4}q^{4}+(-3^{3}+\cdots)q^{5}+\cdots\)
182.6.a.e	$182$	$6$	182.a	1.a	$1$	$3$	$3$	$29.190$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$1$	\(-12\)	\(-14\)	\(-27\)	\(-147\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-4q^{2}+(-5+\beta _{1})q^{3}+2^{4}q^{4}+(-9+\cdots)q^{5}+\cdots\)
182.6.a.f	$182$	$6$	182.a	1.a	$1$	$3$	$3$	$29.190$	3.3.912300.1	None	✓	$1$	$1$	\(12\)	\(-22\)	\(-83\)	\(147\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+4q^{2}+(-7-\beta _{1})q^{3}+2^{4}q^{4}+(-28+\cdots)q^{5}+\cdots\)
182.6.a.g	$182$	$6$	182.a	1.a	$1$	$4$	$4$	$29.190$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	$1$	$0$	\(-16\)	\(-5\)	\(47\)	\(-196\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-4q^{2}+(-1-\beta _{1})q^{3}+2^{4}q^{4}+(12+\cdots)q^{5}+\cdots\)
182.6.a.h	$182$	$6$	182.a	1.a	$1$	$4$	$4$	$29.190$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	$1$	$0$	\(-16\)	\(13\)	\(-55\)	\(196\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-4q^{2}+(3+\beta _{1})q^{3}+2^{4}q^{4}+(-14+\cdots)q^{5}+\cdots\)
182.6.a.i	$182$	$6$	182.a	1.a	$1$	$5$	$5$	$29.190$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	$1$	$0$	\(20\)	\(5\)	\(-49\)	\(-245\)		$-$	$+$	$+$	$-$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q+4q^{2}+(1+\beta _{1})q^{3}+2^{4}q^{4}+(-10+\cdots)q^{5}+\cdots\)
182.6.a.j	$182$	$6$	182.a	1.a	$1$	$5$	$5$	$29.190$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	$1$	$0$	\(20\)	\(23\)	\(41\)	\(245\)		$-$	$-$	$-$	$-$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q+4q^{2}+(5-\beta _{1})q^{3}+2^{4}q^{4}+(8+\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(182))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(182)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(13))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 2}\)