Space of modular forms of level 114, weight 6, and trivial character

• Label: 114.6.a
• Level: $114$
• Weight: $6$
• Character orbit: 114.a
• Rep. character: $\chi_{114}(1,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $9$
• Sturm bound: $120$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 114 = 2 \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	114.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(120\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(114))\).

	Total	New	Old
Modular forms	104	16	88
Cusp forms	96	16	80
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.

\(2\)	\(3\)	\(19\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(2\)
\(+\)	\(+\)	\(-\)	$-$	\(3\)
\(+\)	\(-\)	\(+\)	$-$	\(2\)
\(+\)	\(-\)	\(-\)	$+$	\(2\)
\(-\)	\(+\)	\(+\)	$-$	\(2\)
\(-\)	\(+\)	\(-\)	$+$	\(1\)
\(-\)	\(-\)	\(+\)	$+$	\(1\)
\(-\)	\(-\)	\(-\)	$-$	\(3\)
Plus space			\(+\)	\(6\)
Minus space			\(-\)	\(10\)

Trace form

\( 16 q - 8 q^{2} + 256 q^{4} + 88 q^{5} + 72 q^{6} - 312 q^{7} - 128 q^{8} + 1296 q^{9} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(114))\) 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	3	19
114.6.a.a	$114$	$6$	114.a	1.a	$1$	$1$	$1$	$18.284$	\(\Q\)	None	✓	$1$	$1$	\(-4\)	\(9\)	\(-54\)	\(104\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{2}+9q^{3}+2^{4}q^{4}-54q^{5}-6^{2}q^{6}+\cdots\)
114.6.a.b	$114$	$6$	114.a	1.a	$1$	$1$	$1$	$18.284$	\(\Q\)	None	✓	$1$	$1$	\(-4\)	\(9\)	\(81\)	\(-247\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{2}+9q^{3}+2^{4}q^{4}+3^{4}q^{5}-6^{2}q^{6}+\cdots\)
114.6.a.c	$114$	$6$	114.a	1.a	$1$	$1$	$1$	$18.284$	\(\Q\)	None	✓	$1$	$1$	\(4\)	\(-9\)	\(21\)	\(-143\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+4q^{2}-9q^{3}+2^{4}q^{4}+21q^{5}-6^{2}q^{6}+\cdots\)
114.6.a.d	$114$	$6$	114.a	1.a	$1$	$1$	$1$	$18.284$	\(\Q\)	None	✓	$1$	$1$	\(4\)	\(9\)	\(-91\)	\(-33\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+4q^{2}+9q^{3}+2^{4}q^{4}-91q^{5}+6^{2}q^{6}+\cdots\)
114.6.a.e	$114$	$6$	114.a	1.a	$1$	$2$	$2$	$18.284$	\(\Q(\sqrt{201}) \)	None	✓	$1$	$1$	\(-8\)	\(-18\)	\(-13\)	\(-33\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{2}-9q^{3}+2^{4}q^{4}+(-4-5\beta )q^{5}+\cdots\)
114.6.a.f	$114$	$6$	114.a	1.a	$1$	$2$	$2$	$18.284$	\(\Q(\sqrt{4089}) \)	None	✓	$1$	$0$	\(-8\)	\(18\)	\(-49\)	\(-105\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{2}+9q^{3}+2^{4}q^{4}+(-24-\beta )q^{5}+\cdots\)
114.6.a.g	$114$	$6$	114.a	1.a	$1$	$2$	$2$	$18.284$	\(\Q(\sqrt{2441}) \)	None	✓	$1$	$0$	\(8\)	\(-18\)	\(-5\)	\(-105\)		$-$	$+$	$+$	$-$	$3$	$\mathrm{SU}(2)$	\(q+4q^{2}-9q^{3}+2^{4}q^{4}+(-3-\beta )q^{5}+\cdots\)
114.6.a.h	$114$	$6$	114.a	1.a	$1$	$3$	$3$	$18.284$	3.3.2922585.1	None	✓	$1$	$0$	\(-12\)	\(-27\)	\(63\)	\(125\)		$+$	$+$	$-$	$-$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q-4q^{2}-9q^{3}+2^{4}q^{4}+(21+\beta _{1}-\beta _{2})q^{5}+\cdots\)
114.6.a.i	$114$	$6$	114.a	1.a	$1$	$3$	$3$	$18.284$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$0$	\(12\)	\(27\)	\(135\)	\(125\)		$-$	$-$	$-$	$-$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q+4q^{2}+9q^{3}+2^{4}q^{4}+(45-\beta _{1})q^{5}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(114))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(114)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 2}\)