Space of modular forms of level 1694, weight 2, and Character 1694.c

• Label: 1694.2.c
• Level: $1694$
• Weight: $2$
• Character orbit: 1694.c
• Rep. character: $\chi_{1694}(1693,\cdot)$
• Character field: $\Q$
• Dimension: $72$
• Newform subspaces: $3$
• Sturm bound: $528$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 1694 = 2 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1694.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 77 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(528\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1694, [\chi])\).

	Total	New	Old
Modular forms	288	72	216
Cusp forms	240	72	168
Eisenstein series	48	0	48

Trace form

\( 72 q - 72 q^{4} - 64 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1694, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1694.2.c.a	$1694$	$2$	1694.c	77.b	$2$	$8$	$8$	$13.527$	\(\Q(\zeta_{16})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{16}q^{2}+\zeta_{16}^{2}q^{3}-q^{4}+\zeta_{16}^{2}q^{5}+\cdots\)
1694.2.c.b	$1694$	$2$	1694.c	77.b	$2$	$32$	$32$	$13.527$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
1694.2.c.c	$1694$	$2$	1694.c	77.b	$2$	$32$	$32$	$13.527$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1694, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1694, [\chi]) \cong \)