Space of modular forms of level 176, weight 2, and trivial character

• Label: 176.2.a
• Level: $176$
• Weight: $2$
• Character orbit: 176.a
• Rep. character: $\chi_{176}(1,\cdot)$
• Character field: $\Q$
• Dimension: $5$
• Newform subspaces: $4$
• Sturm bound: $48$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 176 = 2^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	176.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(48\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(176))\).

	Total	New	Old
Modular forms	30	5	25
Cusp forms	19	5	14
Eisenstein series	11	0	11

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

\(2\)	\(11\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(6\)	\(0\)	\(6\)		\(4\)	\(0\)	\(4\)		\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(-\)		\(9\)	\(3\)	\(6\)		\(6\)	\(3\)	\(3\)		\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(-\)		\(9\)	\(1\)	\(8\)		\(6\)	\(1\)	\(5\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(+\)		\(6\)	\(1\)	\(5\)		\(3\)	\(1\)	\(2\)		\(3\)	\(0\)	\(3\)
Plus space		\(+\)		\(12\)	\(1\)	\(11\)		\(7\)	\(1\)	\(6\)		\(5\)	\(0\)	\(5\)
Minus space		\(-\)		\(18\)	\(4\)	\(14\)		\(12\)	\(4\)	\(8\)		\(6\)	\(0\)	\(6\)

Trace form

5 * q + 2 * q^3 - 2 * q^5 + 4 * q^7 + 5 * q^9 + 3 * q^11 - 2 * q^13 + 2 * q^15 + 2 * q^17 - 4 * q^19 - 8 * q^21 - 6 * q^23 + 7 * q^25 + 2 * q^27 - 10 * q^29 + 2 * q^31 - 12 * q^35 - 10 * q^37 - 8 * q^39 + 2 * q^41 + 16 * q^43 - 18 * q^45 - 16 * q^47 + 13 * q^49 - 28 * q^51 - 2 * q^53 - 4 * q^55 - 8 * q^57 - 2 * q^59 + 6 * q^61 + 32 * q^63 - 4 * q^65 - 2 * q^67 + 8 * q^69 - 10 * q^71 + 18 * q^73 + 28 * q^75 + 20 * q^79 - 3 * q^81 - 8 * q^83 + 4 * q^85 - 40 * q^87 + 14 * q^89 + 48 * q^91 + 24 * q^93 + 48 * q^95 + 6 * q^97 + 9 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(176))\) 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	11
176.2.a.a	$176$	$2$	176.a	1.a	$1$	$1$	$1$	$1.405$	\(\Q\)	None	✓		✓	✓	44.2.a.a	$1$	$1$	\(0\)	\(-1\)	\(-3\)	\(-2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{5}-2q^{7}-2q^{9}+q^{11}+\cdots\)
176.2.a.b	$176$	$2$	176.a	1.a	$1$	$1$	$1$	$1.405$	\(\Q\)	None	✓		✓	✓	11.2.a.a	$1$	$0$	\(0\)	\(1\)	\(1\)	\(2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+2q^{7}-2q^{9}-q^{11}+4q^{13}+\cdots\)
176.2.a.c	$176$	$2$	176.a	1.a	$1$	$1$	$1$	$1.405$	\(\Q\)	None	✓				88.2.a.a	$1$	$0$	\(0\)	\(3\)	\(-3\)	\(2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-3q^{5}+2q^{7}+6q^{9}+q^{11}+\cdots\)
176.2.a.d	$176$	$2$	176.a	1.a	$1$	$2$	$2$	$1.405$	\(\Q(\sqrt{17}) \)	None	✓		✓		88.2.a.b	$1$	$0$	\(0\)	\(-1\)	\(3\)	\(2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+(2-\beta )q^{5}+2\beta q^{7}+(1+\beta )q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(176))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(176)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 2}\)