Space of modular forms of level 552, weight 2, and trivial character

• Label: 552.2.a
• Level: $552$
• Weight: $2$
• Character orbit: 552.a
• Rep. character: $\chi_{552}(1,\cdot)$
• Character field: $\Q$
• Dimension: $10$
• Newform subspaces: $7$
• Sturm bound: $192$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(192\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(552))\).

	Total	New	Old
Modular forms	104	10	94
Cusp forms	89	10	79
Eisenstein series	15	0	15

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

\(2\)	\(3\)	\(23\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(9\)	\(1\)	\(8\)		\(8\)	\(1\)	\(7\)		\(1\)	\(0\)	\(1\)
\(+\)	\(+\)	\(-\)	\(-\)		\(17\)	\(2\)	\(15\)		\(15\)	\(2\)	\(13\)		\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(+\)	\(-\)		\(11\)	\(3\)	\(8\)		\(9\)	\(3\)	\(6\)		\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(-\)	\(+\)		\(15\)	\(0\)	\(15\)		\(13\)	\(0\)	\(13\)		\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(+\)	\(-\)		\(11\)	\(0\)	\(11\)		\(9\)	\(0\)	\(9\)		\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(-\)	\(+\)		\(15\)	\(1\)	\(14\)		\(13\)	\(1\)	\(12\)		\(2\)	\(0\)	\(2\)
\(-\)	\(-\)	\(+\)	\(+\)		\(9\)	\(1\)	\(8\)		\(7\)	\(1\)	\(6\)		\(2\)	\(0\)	\(2\)
\(-\)	\(-\)	\(-\)	\(-\)		\(17\)	\(2\)	\(15\)		\(15\)	\(2\)	\(13\)		\(2\)	\(0\)	\(2\)
Plus space			\(+\)		\(48\)	\(3\)	\(45\)		\(41\)	\(3\)	\(38\)		\(7\)	\(0\)	\(7\)
Minus space			\(-\)		\(56\)	\(7\)	\(49\)		\(48\)	\(7\)	\(41\)		\(8\)	\(0\)	\(8\)

Trace form

10 * q + 2 * q^3 + 4 * q^5 + 10 * q^9 + 4 * q^13 - 4 * q^15 - 4 * q^17 + 4 * q^19 + 4 * q^21 + 22 * q^25 + 2 * q^27 - 12 * q^29 + 12 * q^33 + 8 * q^37 + 4 * q^39 - 4 * q^41 + 4 * q^43 + 4 * q^45 - 8 * q^47 + 10 * q^49 + 12 * q^53 - 16 * q^55 + 4 * q^57 - 8 * q^59 + 24 * q^61 - 8 * q^65 - 4 * q^67 - 4 * q^69 - 24 * q^71 + 4 * q^73 + 14 * q^75 + 10 * q^81 - 24 * q^83 - 24 * q^85 - 12 * q^87 - 36 * q^89 + 16 * q^91 - 56 * q^95 + 12 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(552))\) 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	3	23
552.2.a.a	$552$	$2$	552.a	1.a	$1$	$1$	$1$	$4.408$	\(\Q\)	None	✓	✓	✓	✓	552.2.a.a	$1$	$1$	\(0\)	\(-1\)	\(-2\)	\(2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+2q^{7}+q^{9}-2q^{11}+\cdots\)
552.2.a.b	$552$	$2$	552.a	1.a	$1$	$1$	$1$	$4.408$	\(\Q\)	None	✓	✓			552.2.a.b	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{7}+q^{9}+2q^{13}+8q^{17}+\cdots\)
552.2.a.c	$552$	$2$	552.a	1.a	$1$	$1$	$1$	$4.408$	\(\Q\)	None	✓	✓	✓	✓	552.2.a.c	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}-4q^{7}+q^{9}-4q^{11}+\cdots\)
552.2.a.d	$552$	$2$	552.a	1.a	$1$	$1$	$1$	$4.408$	\(\Q\)	None	✓	✓			552.2.a.d	$1$	$0$	\(0\)	\(-1\)	\(4\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+4q^{5}+2q^{7}+q^{9}+2q^{13}+\cdots\)
552.2.a.e	$552$	$2$	552.a	1.a	$1$	$1$	$1$	$4.408$	\(\Q\)	None	✓	✓	✓	✓	552.2.a.e	$1$	$1$	\(0\)	\(1\)	\(-2\)	\(-4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}-4q^{7}+q^{9}-2q^{13}+\cdots\)
552.2.a.f	$552$	$2$	552.a	1.a	$1$	$2$	$2$	$4.408$	\(\Q(\sqrt{5}) \)	None	✓	✓	✓	✓	552.2.a.f	$1$	$0$	\(0\)	\(2\)	\(2\)	\(4\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+(1+\beta )q^{5}+2q^{7}+q^{9}+(1+\beta )q^{11}+\cdots\)
552.2.a.g	$552$	$2$	552.a	1.a	$1$	$3$	$3$	$4.408$	3.3.148.1	None	✓	✓	✓	✓	552.2.a.g	$1$	$0$	\(0\)	\(3\)	\(0\)	\(2\)		$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta _{2}q^{5}+(1+\beta _{1})q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(552))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(552)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(138))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(184))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(276))\)\(^{\oplus 2}\)