Space of modular forms of level 544, weight 2, and trivial character

• Label: 544.2.a
• Level: $544$
• Weight: $2$
• Character orbit: 544.a
• Rep. character: $\chi_{544}(1,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $10$
• Sturm bound: $144$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 544 = 2^{5} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	544.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(144\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\), \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(544))\).

	Total	New	Old
Modular forms	80	16	64
Cusp forms	65	16	49
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.

\(2\)	\(17\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(17\)	\(3\)	\(14\)		\(14\)	\(3\)	\(11\)		\(3\)	\(0\)	\(3\)
\(+\)	\(-\)	\(-\)		\(21\)	\(5\)	\(16\)		\(17\)	\(5\)	\(12\)		\(4\)	\(0\)	\(4\)
\(-\)	\(+\)	\(-\)		\(23\)	\(5\)	\(18\)		\(19\)	\(5\)	\(14\)		\(4\)	\(0\)	\(4\)
\(-\)	\(-\)	\(+\)		\(19\)	\(3\)	\(16\)		\(15\)	\(3\)	\(12\)		\(4\)	\(0\)	\(4\)
Plus space		\(+\)		\(36\)	\(6\)	\(30\)		\(29\)	\(6\)	\(23\)		\(7\)	\(0\)	\(7\)
Minus space		\(-\)		\(44\)	\(10\)	\(34\)		\(36\)	\(10\)	\(26\)		\(8\)	\(0\)	\(8\)

Trace form

16 * q + 16 * q^9 - 16 * q^13 + 32 * q^25 + 16 * q^29 + 16 * q^33 - 16 * q^37 + 16 * q^41 - 32 * q^45 + 32 * q^49 - 48 * q^53 + 16 * q^57 - 16 * q^61 + 48 * q^65 - 16 * q^69 + 16 * q^77 - 16 * q^89 - 48 * q^93 - 48 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(544))\) 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	17
544.2.a.a	$544$	$2$	544.a	1.a	$1$	$1$	$1$	$4.344$	\(\Q\)	None	✓	✓			544.2.a.a	$1$	$0$	\(0\)	\(-2\)	\(2\)	\(-2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+2q^{5}-2q^{7}+q^{9}+2q^{11}+\cdots\)
544.2.a.b	$544$	$2$	544.a	1.a	$1$	$1$	$1$	$4.344$	\(\Q\)	None	✓	✓			544.2.a.b	$1$	$0$	\(0\)	\(-2\)	\(4\)	\(4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+4q^{5}+4q^{7}+q^{9}-2q^{11}+\cdots\)
544.2.a.c	$544$	$2$	544.a	1.a	$1$	$1$	$1$	$4.344$	\(\Q\)	None	✓	✓			544.2.a.c	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}-3q^{9}-4q^{11}+2q^{13}-q^{17}+\cdots\)
544.2.a.d	$544$	$2$	544.a	1.a	$1$	$1$	$1$	$4.344$	\(\Q\)	None	✓	✓			544.2.a.c	$1$	$0$	\(0\)	\(0\)	\(0\)	\(2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}-3q^{9}+4q^{11}+2q^{13}-q^{17}+\cdots\)
544.2.a.e	$544$	$2$	544.a	1.a	$1$	$1$	$1$	$4.344$	\(\Q\)	None	✓	✓			544.2.a.a	$1$	$0$	\(0\)	\(2\)	\(2\)	\(2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+2q^{5}+2q^{7}+q^{9}-2q^{11}+\cdots\)
544.2.a.f	$544$	$2$	544.a	1.a	$1$	$1$	$1$	$4.344$	\(\Q\)	None	✓	✓			544.2.a.b	$1$	$0$	\(0\)	\(2\)	\(4\)	\(-4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+4q^{5}-4q^{7}+q^{9}+2q^{11}+\cdots\)
544.2.a.g	$544$	$2$	544.a	1.a	$1$	$2$	$2$	$4.344$	\(\Q(\sqrt{2}) \)	None	✓	✓	✓		544.2.a.g	$2$	$1$	\(0\)	\(0\)	\(-4\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-2q^{5}-3\beta q^{7}-q^{9}+\beta q^{11}+\cdots\)
544.2.a.h	$544$	$2$	544.a	1.a	$1$	$2$	$2$	$4.344$	\(\Q(\sqrt{10}) \)	None	✓	✓	✓		544.2.a.h	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-2q^{5}+\beta q^{7}+7q^{9}+\beta q^{11}+\cdots\)
544.2.a.i	$544$	$2$	544.a	1.a	$1$	$3$	$3$	$4.344$	3.3.148.1	None	✓	✓	✓	✓	544.2.a.i	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(-2\)		$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+(-\beta _{1}-\beta _{2})q^{5}+(-1+\cdots)q^{7}+\cdots\)
544.2.a.j	$544$	$2$	544.a	1.a	$1$	$3$	$3$	$4.344$	3.3.148.1	None	✓	✓	✓		544.2.a.i	$1$	$0$	\(0\)	\(2\)	\(-2\)	\(2\)		$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+(-\beta _{1}-\beta _{2})q^{5}+(1-\beta _{2})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(544))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(544)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(68))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(136))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(272))\)\(^{\oplus 2}\)