Space of modular forms of level 1573, weight 4, and trivial character

• Label: 1573.4.a
• Level: $1573$
• Weight: $4$
• Character orbit: 1573.a
• Rep. character: $\chi_{1573}(1,\cdot)$
• Character field: $\Q$
• Dimension: $327$
• Newform subspaces: $18$
• Sturm bound: $616$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1573 = 11^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1573.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 18 \)
Sturm bound:			\(616\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(1573))\).

	Total	New	Old
Modular forms	474	327	147
Cusp forms	450	327	123
Eisenstein series	24	0	24

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

\(11\)	\(13\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(83\)
\(+\)	\(-\)	$-$	\(79\)
\(-\)	\(+\)	$-$	\(80\)
\(-\)	\(-\)	$+$	\(85\)
Plus space		\(+\)	\(168\)
Minus space		\(-\)	\(159\)

Trace form

\( 327 q + 4 q^{2} + 2 q^{3} + 1286 q^{4} - 10 q^{5} - 4 q^{6} + 22 q^{7} - 36 q^{8} + 2969 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(1573))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		11	13
1573.4.a.a	$1573$	$4$	1573.a	1.a	$1$	$1$	$1$	$92.810$	\(\Q\)	None	✓	$1$	$1$	\(5\)	\(-7\)	\(-7\)	\(13\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+5q^{2}-7q^{3}+17q^{4}-7q^{5}-35q^{6}+\cdots\)
1573.4.a.b	$1573$	$4$	1573.a	1.a	$1$	$2$	$2$	$92.810$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(-1\)	\(5\)	\(-3\)	\(9\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(4-3\beta )q^{3}+(-4+\beta )q^{4}+\cdots\)
1573.4.a.c	$1573$	$4$	1573.a	1.a	$1$	$4$	$4$	$92.810$	4.4.297133.1	None	✓	$1$	$1$	\(0\)	\(-4\)	\(-6\)	\(17\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(-1-\beta _{3})q^{3}+(2+\beta _{1}+2\beta _{2}+\cdots)q^{4}+\cdots\)
1573.4.a.d	$1573$	$4$	1573.a	1.a	$1$	$6$	$6$	$92.810$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	$1$	$0$	\(6\)	\(-6\)	\(-8\)	\(53\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(-1-\beta _{4})q^{3}+(4-\beta _{1}+\cdots)q^{4}+\cdots\)
1573.4.a.e	$1573$	$4$	1573.a	1.a	$1$	$9$	$9$	$92.810$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(8\)	\(30\)	\(-25\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1-\beta _{3})q^{3}+(5-\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
1573.4.a.f	$1573$	$4$	1573.a	1.a	$1$	$11$	$11$	$92.810$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	$1$	$1$	\(-6\)	\(6\)	\(-4\)	\(-45\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(1-\beta _{5})q^{3}+(6-\beta _{1}+\cdots)q^{4}+\cdots\)
1573.4.a.g	$1573$	$4$	1573.a	1.a	$1$	$15$	$15$	$92.810$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	$1$	$1$	\(-6\)	\(2\)	\(-14\)	\(-28\)		$+$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{4}q^{3}+(3+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
1573.4.a.h	$1573$	$4$	1573.a	1.a	$1$	$15$	$15$	$92.810$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	$1$	$1$	\(-6\)	\(2\)	\(-2\)	\(-28\)		$-$	$+$	$-$	$2^{5}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{5}q^{3}+(3+\beta _{1}+\beta _{2})q^{4}+\cdots\)
1573.4.a.i	$1573$	$4$	1573.a	1.a	$1$	$15$	$15$	$92.810$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	$1$	$1$	\(-6\)	\(2\)	\(14\)	\(-28\)		$-$	$+$	$-$	$2^{10}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{5}q^{3}+(3+\beta _{1}+\beta _{2})q^{4}+\cdots\)
1573.4.a.j	$1573$	$4$	1573.a	1.a	$1$	$15$	$15$	$92.810$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	$1$	$0$	\(6\)	\(2\)	\(-14\)	\(28\)		$+$	$+$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{4}q^{3}+(3+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
1573.4.a.k	$1573$	$4$	1573.a	1.a	$1$	$15$	$15$	$92.810$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	$1$	$0$	\(6\)	\(2\)	\(-2\)	\(28\)		$-$	$-$	$+$	$2^{5}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{5}q^{3}+(3+\beta _{1}+\beta _{2})q^{4}+\cdots\)
1573.4.a.l	$1573$	$4$	1573.a	1.a	$1$	$15$	$15$	$92.810$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	$1$	$0$	\(6\)	\(2\)	\(14\)	\(28\)		$-$	$-$	$+$	$2^{10}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{5}q^{3}+(3+\beta _{1}+\beta _{2})q^{4}+\cdots\)
1573.4.a.m	$1573$	$4$	1573.a	1.a	$1$	$30$	$30$	$92.810$		None	✓	$1$	$1$	\(-12\)	\(4\)	\(-28\)	\(-56\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
1573.4.a.n	$1573$	$4$	1573.a	1.a	$1$	$30$	$30$	$92.810$		None	✓	$1$	$0$	\(12\)	\(4\)	\(-28\)	\(56\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
1573.4.a.o	$1573$	$4$	1573.a	1.a	$1$	$34$	$34$	$92.810$		None	✓	$1$	$1$	\(-3\)	\(-29\)	\(-28\)	\(-36\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
1573.4.a.p	$1573$	$4$	1573.a	1.a	$1$	$34$	$34$	$92.810$		None	✓	$1$	$1$	\(3\)	\(-29\)	\(-28\)	\(36\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
1573.4.a.q	$1573$	$4$	1573.a	1.a	$1$	$38$	$38$	$92.810$		None	✓	$1$	$0$	\(-3\)	\(19\)	\(52\)	\(-12\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
1573.4.a.r	$1573$	$4$	1573.a	1.a	$1$	$38$	$38$	$92.810$		None	✓	$1$	$0$	\(3\)	\(19\)	\(52\)	\(12\)		$-$	$-$	$+$		$\mathrm{SU}(2)$

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(1573))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(1573)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(13))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(143))\)\(^{\oplus 2}\)