Space of modular forms of level 1216, weight 1, and Character 1216.e

• Label: 1216.1.e
• Level: $1216$
• Weight: $1$
• Character orbit: 1216.e
• Rep. character: $\chi_{1216}(1025,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $2$
• Sturm bound: $160$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 1216 = 2^{6} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1216.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(160\)
Trace bound:			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1216, [\chi])\).

	Total	New	Old
Modular forms	22	4	18
Cusp forms	10	2	8
Eisenstein series	12	2	10

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	2	0	0	0

Trace form

\( 2 q + 2 q^{5} + 2 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1216, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1216.1.e.a	$1216$	$1$	1216.e	19.b	$2$	$1$	$1$	$0.607$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-19}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(1\)	\(-1\)	$1$		\(q+q^{5}-q^{7}+q^{9}+q^{11}-q^{17}-q^{19}+\cdots\)
1216.1.e.b	$1216$	$1$	1216.e	19.b	$2$	$1$	$1$	$0.607$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-19}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(1\)	\(1\)	$1$		\(q+q^{5}+q^{7}+q^{9}-q^{11}-q^{17}+q^{19}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1216, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1216, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(304, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(608, [\chi])\)\(^{\oplus 2}\)