Space of modular forms of level 5571, weight 2, and trivial character

• Label: 5571.2.a
• Level: $5571$
• Weight: $2$
• Character orbit: 5571.a
• Rep. character: $\chi_{5571}(1,\cdot)$
• Character field: $\Q$
• Dimension: $258$
• Newform subspaces: $10$
• Sturm bound: $1240$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 5571 = 3^{2} \cdot 619 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5571.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(1240\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5571))\).

	Total	New	Old
Modular forms	624	258	366
Cusp forms	617	258	359
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.

\(3\)	\(619\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(42\)
\(+\)	\(-\)	$-$	\(62\)
\(-\)	\(+\)	$-$	\(82\)
\(-\)	\(-\)	$+$	\(72\)
Plus space		\(+\)	\(114\)
Minus space		\(-\)	\(144\)

Trace form

\( 258 q + 3 q^{2} + 261 q^{4} + 2 q^{5} - 2 q^{7} + 9 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5571))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	619
5571.2.a.a	$5571$	$2$	5571.a	1.a	$1$	$1$	$1$	$44.485$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(3\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}+3q^{5}+2q^{11}+4q^{13}+4q^{16}+\cdots\)
5571.2.a.b	$5571$	$2$	5571.a	1.a	$1$	$2$	$2$	$44.485$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(1\)	\(-1\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+(1-\beta )q^{5}+(-2+3\beta )q^{7}+\cdots\)
5571.2.a.c	$5571$	$2$	5571.a	1.a	$1$	$19$	$19$	$44.485$	\(\mathbb{Q}[x]/(x^{19} - \cdots)\)	None	✓	$1$	$1$	\(5\)	\(0\)	\(6\)	\(-27\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}+\beta _{17}q^{5}+(-1+\beta _{9}+\cdots)q^{7}+\cdots\)
5571.2.a.d	$5571$	$2$	5571.a	1.a	$1$	$21$	$21$	$44.485$		None	✓	$1$	$1$	\(-3\)	\(0\)	\(-9\)	\(18\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
5571.2.a.e	$5571$	$2$	5571.a	1.a	$1$	$21$	$21$	$44.485$		None	✓	$1$	$0$	\(9\)	\(0\)	\(21\)	\(-4\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
5571.2.a.f	$5571$	$2$	5571.a	1.a	$1$	$27$	$27$	$44.485$		None	✓	$1$	$0$	\(7\)	\(0\)	\(5\)	\(-21\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
5571.2.a.g	$5571$	$2$	5571.a	1.a	$1$	$30$	$30$	$44.485$		None	✓	$1$	$1$	\(-9\)	\(0\)	\(-21\)	\(2\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
5571.2.a.h	$5571$	$2$	5571.a	1.a	$1$	$33$	$33$	$44.485$		None	✓	$1$	$0$	\(-4\)	\(0\)	\(-4\)	\(31\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
5571.2.a.i	$5571$	$2$	5571.a	1.a	$1$	$42$	$42$	$44.485$		None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-14\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
5571.2.a.j	$5571$	$2$	5571.a	1.a	$1$	$62$	$62$	$44.485$		None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(14\)		$+$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5571))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5571)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(619))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1857))\)\(^{\oplus 2}\)