Space of modular forms of level 2151, weight 4, and trivial character

• Label: 2151.4.a
• Level: $2151$
• Weight: $4$
• Character orbit: 2151.a
• Rep. character: $\chi_{2151}(1,\cdot)$
• Character field: $\Q$
• Dimension: $297$
• Newform subspaces: $8$
• Sturm bound: $960$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 2151 = 3^{2} \cdot 239 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2151.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(960\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(2151))\).

	Total	New	Old
Modular forms	724	297	427
Cusp forms	716	297	419
Eisenstein series	8	0	8

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

\(3\)	\(239\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(59\)
\(+\)	\(-\)	$-$	\(59\)
\(-\)	\(+\)	$-$	\(82\)
\(-\)	\(-\)	$+$	\(97\)
Plus space		\(+\)	\(156\)
Minus space		\(-\)	\(141\)

Trace form

\( 297 q + 4 q^{2} + 1196 q^{4} + 10 q^{5} - 32 q^{7} + 6 q^{8} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(2151))\) 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	239
2151.4.a.a	$2151$	$4$	2151.a	1.a	$1$	$22$	$22$	$126.913$		None	✓	$1$	$1$	\(4\)	\(0\)	\(37\)	\(-52\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
2151.4.a.b	$2151$	$4$	2151.a	1.a	$1$	$28$	$28$	$126.913$		None	✓	$1$	$1$	\(5\)	\(0\)	\(-6\)	\(-68\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
2151.4.a.c	$2151$	$4$	2151.a	1.a	$1$	$28$	$28$	$126.913$		None	✓	$1$	$0$	\(13\)	\(0\)	\(74\)	\(-82\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
2151.4.a.d	$2151$	$4$	2151.a	1.a	$1$	$32$	$32$	$126.913$		None	✓	$1$	$1$	\(-11\)	\(0\)	\(-66\)	\(58\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
2151.4.a.e	$2151$	$4$	2151.a	1.a	$1$	$32$	$32$	$126.913$		None	✓	$1$	$0$	\(-3\)	\(0\)	\(14\)	\(72\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
2151.4.a.f	$2151$	$4$	2151.a	1.a	$1$	$37$	$37$	$126.913$		None	✓	$1$	$0$	\(-4\)	\(0\)	\(-43\)	\(60\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
2151.4.a.g	$2151$	$4$	2151.a	1.a	$1$	$59$	$59$	$126.913$		None	✓	$1$	$1$	\(-8\)	\(0\)	\(-80\)	\(-10\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
2151.4.a.h	$2151$	$4$	2151.a	1.a	$1$	$59$	$59$	$126.913$		None	✓	$1$	$0$	\(8\)	\(0\)	\(80\)	\(-10\)		$+$	$+$	$+$		$\mathrm{SU}(2)$

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(2151))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(2151)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(239))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(717))\)\(^{\oplus 2}\)