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		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(1\)	\(0\)	\(1\)		\(1\)	\(0\)	\(1\)		\(0\)	\(0\)	\(0\)
\(+\)	\(+\)	\(-\)	\(-\)		\(6\)	\(1\)	\(5\)		\(5\)	\(1\)	\(4\)		\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(+\)	\(-\)		\(5\)	\(1\)	\(4\)		\(4\)	\(1\)	\(3\)		\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(-\)	\(+\)		\(4\)	\(0\)	\(4\)		\(3\)	\(0\)	\(3\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(+\)	\(-\)		\(5\)	\(2\)	\(3\)		\(4\)	\(2\)	\(2\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)	\(+\)		\(4\)	\(0\)	\(4\)		\(3\)	\(0\)	\(3\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)	\(+\)		\(4\)	\(0\)	\(4\)		\(3\)	\(0\)	\(3\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(-\)	\(-\)		\(3\)	\(1\)	\(2\)		\(2\)	\(1\)	\(1\)		\(1\)	\(0\)	\(1\)
Plus space			\(+\)		\(13\)	\(0\)	\(13\)		\(10\)	\(0\)	\(10\)		\(3\)	\(0\)	\(3\)
Minus space			\(-\)		\(19\)	\(5\)	\(14\)		\(15\)	\(5\)	\(10\)		\(4\)	\(0\)	\(4\)

Trace form

5 * q + q^2 + 8 * q^3 + 5 * q^4 + 2 * q^5 - q^7 + q^8 + 5 * q^9 - 6 * q^10 - 4 * q^11 + 8 * q^12 - q^13 - q^14 - 8 * q^15 + 5 * q^16 - 6 * q^17 - 3 * q^18 + 2 * q^20 + 8 * q^22 - 4 * q^23 + 11 * q^25 - q^26 + 8 * q^27 - q^28 - 18 * q^29 - 16 * q^30 + 8 * q^31 + q^32 - 16 * q^33 - 6 * q^34 - 2 * q^35 + 5 * q^36 + 22 * q^37 - 8 * q^38 - 4 * q^39 - 6 * q^40 - 22 * q^41 - 4 * q^42 - 4 * q^43 - 4 * q^44 - 38 * q^45 - 8 * q^47 + 8 * q^48 + 5 * q^49 - q^50 - 8 * q^51 - q^52 - 10 * q^53 - q^56 - 8 * q^57 - 10 * q^58 - 8 * q^59 - 8 * q^60 + 10 * q^61 + 3 * q^63 + 5 * q^64 + 6 * q^65 + 16 * q^66 + 28 * q^67 - 6 * q^68 - 16 * q^69 + 6 * q^70 + 24 * q^71 - 3 * q^72 + 34 * q^73 - 6 * q^74 + 24 * q^75 - 12 * q^77 - 12 * q^79 + 2 * q^80 + 29 * q^81 + 10 * q^82 + 4 * q^85 + 36 * q^86 - 8 * q^87 + 8 * q^88 + 2 * q^89 - 22 * q^90 + q^91 - 4 * q^92 + 32 * q^93 + 32 * q^95 + 34 * q^97 + q^98 - 28 * q^99

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	Twist minimal	Largest	Maximal	Minimal twist	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	✓	✓	✓	✓	182.2.a.a	$1$	$0$	\(-1\)	\(1\)	\(4\)	\(-1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+4q^{5}-q^{6}-q^{7}+\cdots\)
182.2.a.b	$182$	$2$	182.a	1.a	$1$	$1$	$1$	$1.453$	\(\Q\)	None	✓	✓	✓	✓	182.2.a.b	$1$	$0$	\(-1\)	\(3\)	\(0\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+3q^{3}+q^{4}-3q^{6}+q^{7}-q^{8}+\cdots\)
182.2.a.c	$182$	$2$	182.a	1.a	$1$	$1$	$1$	$1.453$	\(\Q\)	None	✓	✓			182.2.a.c	$1$	$0$	\(1\)	\(0\)	\(2\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+2q^{5}-q^{7}+q^{8}-3q^{9}+\cdots\)
182.2.a.d	$182$	$2$	182.a	1.a	$1$	$1$	$1$	$1.453$	\(\Q\)	None	✓	✓	✓	✓	182.2.a.d	$1$	$0$	\(1\)	\(1\)	\(0\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{7}+q^{8}+\cdots\)
182.2.a.e	$182$	$2$	182.a	1.a	$1$	$1$	$1$	$1.453$	\(\Q\)	None	✓	✓			182.2.a.e	$1$	$0$	\(1\)	\(3\)	\(-4\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+3q^{3}+q^{4}-4q^{5}+3q^{6}-q^{7}+\cdots\)

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

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