Space of modular forms of level 574, weight 2, and trivial character

• Label: 574.2.a
• Level: $574$
• Weight: $2$
• Character orbit: 574.a
• Rep. character: $\chi_{574}(1,\cdot)$
• Character field: $\Q$
• Dimension: $19$
• Newform subspaces: $13$
• Sturm bound: $168$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 574 = 2 \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	574.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 13 \)
Sturm bound:			\(168\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\), \(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(574))\).

	Total	New	Old
Modular forms	88	19	69
Cusp forms	81	19	62
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.

\(2\)	\(7\)	\(41\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(2\)
\(+\)	\(+\)	\(-\)	$-$	\(4\)
\(+\)	\(-\)	\(+\)	$-$	\(3\)
\(+\)	\(-\)	\(-\)	$+$	\(1\)
\(-\)	\(+\)	\(+\)	$-$	\(3\)
\(-\)	\(+\)	\(-\)	$+$	\(1\)
\(-\)	\(-\)	\(+\)	$+$	\(2\)
\(-\)	\(-\)	\(-\)	$-$	\(3\)
Plus space			\(+\)	\(6\)
Minus space			\(-\)	\(13\)

Trace form

\( 19 q - q^{2} + 4 q^{3} + 19 q^{4} + 2 q^{5} - 4 q^{6} - q^{7} - q^{8} + 23 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(574))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	7	41
574.2.a.a	$574$	$2$	574.a	1.a	$1$	$1$	$1$	$4.583$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(-2\)	\(4\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-2q^{3}+q^{4}+4q^{5}+2q^{6}+q^{7}+\cdots\)
574.2.a.b	$574$	$2$	574.a	1.a	$1$	$1$	$1$	$4.583$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(-1\)	\(1\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{7}+\cdots\)
574.2.a.c	$574$	$2$	574.a	1.a	$1$	$1$	$1$	$4.583$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(1\)	\(-3\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}+q^{7}+\cdots\)
574.2.a.d	$574$	$2$	574.a	1.a	$1$	$1$	$1$	$4.583$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(2\)	\(-2\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+2q^{3}+q^{4}-2q^{5}-2q^{6}-q^{7}+\cdots\)
574.2.a.e	$574$	$2$	574.a	1.a	$1$	$1$	$1$	$4.583$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(2\)	\(2\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+2q^{3}+q^{4}+2q^{5}-2q^{6}+q^{7}+\cdots\)
574.2.a.f	$574$	$2$	574.a	1.a	$1$	$1$	$1$	$4.583$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(3\)	\(-1\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+3q^{3}+q^{4}-q^{5}-3q^{6}+q^{7}+\cdots\)
574.2.a.g	$574$	$2$	574.a	1.a	$1$	$1$	$1$	$4.583$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(-3\)	\(-1\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-3q^{3}+q^{4}-q^{5}-3q^{6}+q^{7}+\cdots\)
574.2.a.h	$574$	$2$	574.a	1.a	$1$	$1$	$1$	$4.583$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(-1\)	\(-1\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots\)
574.2.a.i	$574$	$2$	574.a	1.a	$1$	$1$	$1$	$4.583$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(-1\)	\(1\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots\)
574.2.a.j	$574$	$2$	574.a	1.a	$1$	$1$	$1$	$4.583$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(-4\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-4q^{5}+q^{7}+q^{8}-3q^{9}+\cdots\)
574.2.a.k	$574$	$2$	574.a	1.a	$1$	$2$	$2$	$4.583$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(2\)	\(4\)	\(2\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+2q^{3}+q^{4}+(1+\beta )q^{5}+2q^{6}+\cdots\)
574.2.a.l	$574$	$2$	574.a	1.a	$1$	$3$	$3$	$4.583$	3.3.568.1	None	✓	$1$	$0$	\(3\)	\(1\)	\(1\)	\(-3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-\beta _{2}q^{3}+q^{4}+\beta _{1}q^{5}-\beta _{2}q^{6}+\cdots\)
574.2.a.m	$574$	$2$	574.a	1.a	$1$	$4$	$4$	$4.583$	4.4.11348.1	None	✓	$1$	$0$	\(-4\)	\(-1\)	\(3\)	\(-4\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}-\beta _{2}q^{3}+q^{4}+(1-\beta _{2}+\beta _{3})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(574))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(574)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(41))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(82))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(287))\)\(^{\oplus 2}\)