Space of modular forms of level 182, weight 2, and trivial character

• Label: 182.2.a
• Level: $182$
• Weight: $2$
• Character orbit: 182.a
• Rep. character: $\chi_{182}(1,\cdot)$
• Character field: $\Q$
• Dimension: $5$
• Newform subspaces: $5$
• Sturm bound: $56$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 182 = 2 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	182.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(56\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(182))\).

	Total	New	Old
Modular forms	32	5	27
Cusp forms	25	5	20
Eisenstein series	7	0	7

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.
\(+\)	\(+\)	\(-\)	\(-\)	\(1\)
\(+\)	\(-\)	\(+\)	\(-\)	\(1\)
\(-\)	\(+\)	\(+\)	\(-\)	\(2\)
\(-\)	\(-\)	\(-\)	\(-\)	\(1\)
Plus space			\(+\)	\(0\)
Minus space			\(-\)	\(5\)

Trace form

\( 5 q + q^{2} + 8 q^{3} + 5 q^{4} + 2 q^{5} - q^{7} + q^{8} + 5 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(182))\) 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
182.2.a.a	$182$	$2$	182.a	1.a	$1$	$1$	$1$	$1.453$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(1\)	\(4\)	\(-1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+4q^{5}-q^{6}-q^{7}+\cdots\)
182.2.a.b	$182$	$2$	182.a	1.a	$1$	$1$	$1$	$1.453$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(3\)	\(0\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+3q^{3}+q^{4}-3q^{6}+q^{7}-q^{8}+\cdots\)
182.2.a.c	$182$	$2$	182.a	1.a	$1$	$1$	$1$	$1.453$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(2\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+2q^{5}-q^{7}+q^{8}-3q^{9}+\cdots\)
182.2.a.d	$182$	$2$	182.a	1.a	$1$	$1$	$1$	$1.453$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(1\)	\(0\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{7}+q^{8}+\cdots\)
182.2.a.e	$182$	$2$	182.a	1.a	$1$	$1$	$1$	$1.453$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(3\)	\(-4\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+3q^{3}+q^{4}-4q^{5}+3q^{6}-q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(182))\) into lower level spaces

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