Space of modular forms of level 182, weight 4, and trivial character

• Label: 182.4.a
• Level: $182$
• Weight: $4$
• Character orbit: 182.a
• Rep. character: $\chi_{182}(1,\cdot)$
• Character field: $\Q$
• Dimension: $18$
• Newform subspaces: $10$
• Sturm bound: $112$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 182 = 2 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	182.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(112\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(182))\).

	Total	New	Old
Modular forms	88	18	70
Cusp forms	80	18	62
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
\(+\)	\(+\)	\(+\)	$+$	\(3\)
\(+\)	\(+\)	\(-\)	$-$	\(2\)
\(+\)	\(-\)	\(+\)	$-$	\(2\)
\(+\)	\(-\)	\(-\)	$+$	\(3\)
\(-\)	\(+\)	\(+\)	$-$	\(1\)
\(-\)	\(+\)	\(-\)	$+$	\(3\)
\(-\)	\(-\)	\(+\)	$+$	\(3\)
\(-\)	\(-\)	\(-\)	$-$	\(1\)
Plus space			\(+\)	\(12\)
Minus space			\(-\)	\(6\)

Trace form

\( 18 q - 4 q^{2} - 12 q^{3} + 72 q^{4} + 32 q^{5} + 40 q^{6} - 16 q^{8} + 270 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(182))\) 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
182.4.a.a	$182$	$4$	182.a	1.a	$1$	$1$	$1$	$10.738$	\(\Q\)	None	✓	$1$	$0$	\(-2\)	\(7\)	\(0\)	\(7\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+7q^{3}+4q^{4}-14q^{6}+7q^{7}+\cdots\)
182.4.a.b	$182$	$4$	182.a	1.a	$1$	$1$	$1$	$10.738$	\(\Q\)	None	✓	$1$	$1$	\(2\)	\(-8\)	\(3\)	\(7\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}-8q^{3}+4q^{4}+3q^{5}-2^{4}q^{6}+\cdots\)
182.4.a.c	$182$	$4$	182.a	1.a	$1$	$1$	$1$	$10.738$	\(\Q\)	None	✓	$1$	$1$	\(2\)	\(-2\)	\(-5\)	\(-7\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}-2q^{3}+4q^{4}-5q^{5}-4q^{6}+\cdots\)
182.4.a.d	$182$	$4$	182.a	1.a	$1$	$1$	$1$	$10.738$	\(\Q\)	None	✓	$1$	$0$	\(2\)	\(5\)	\(16\)	\(7\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+5q^{3}+4q^{4}+2^{4}q^{5}+10q^{6}+\cdots\)
182.4.a.e	$182$	$4$	182.a	1.a	$1$	$2$	$2$	$10.738$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(-4\)	\(-10\)	\(-8\)	\(14\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+(-5+3\beta )q^{3}+4q^{4}+(-4+\cdots)q^{5}+\cdots\)
182.4.a.f	$182$	$4$	182.a	1.a	$1$	$2$	$2$	$10.738$	\(\Q(\sqrt{1169}) \)	None	✓	$1$	$0$	\(-4\)	\(-8\)	\(5\)	\(14\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-4q^{3}+4q^{4}+(3-\beta )q^{5}+8q^{6}+\cdots\)
182.4.a.g	$182$	$4$	182.a	1.a	$1$	$2$	$2$	$10.738$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(-4\)	\(-4\)	\(6\)	\(-14\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+(-2+3\beta )q^{3}+4q^{4}+(3-\beta )q^{5}+\cdots\)
182.4.a.h	$182$	$4$	182.a	1.a	$1$	$2$	$2$	$10.738$	\(\Q(\sqrt{43}) \)	None	✓	$1$	$0$	\(4\)	\(2\)	\(4\)	\(14\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+(1+\beta )q^{3}+4q^{4}+(2-\beta )q^{5}+\cdots\)
182.4.a.i	$182$	$4$	182.a	1.a	$1$	$3$	$3$	$10.738$	3.3.294825.1	None	✓	$1$	$0$	\(-6\)	\(-1\)	\(13\)	\(-21\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-\beta _{1}q^{3}+4q^{4}+(5-\beta _{1}+\beta _{2})q^{5}+\cdots\)
182.4.a.j	$182$	$4$	182.a	1.a	$1$	$3$	$3$	$10.738$	3.3.842136.1	None	✓	$1$	$0$	\(6\)	\(7\)	\(-2\)	\(-21\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+(2+\beta _{1})q^{3}+4q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(182))\) into lower level spaces

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