Space of modular forms of level 696, weight 2, and Character 696.y

• Label: 696.2.y
• Level: $696$
• Weight: $2$
• Character orbit: 696.y
• Rep. character: $\chi_{696}(25,\cdot)$
• Character field: $\Q(\zeta_{7})$
• Dimension: $96$
• Newform subspaces: $5$
• Sturm bound: $240$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 696 = 2^{3} \cdot 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	696.y (of order \(7\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 29 \)
Character field:			\(\Q(\zeta_{7})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(240\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(696, [\chi])\).

	Total	New	Old
Modular forms	768	96	672
Cusp forms	672	96	576
Eisenstein series	96	0	96

Trace form

\( 96 q + 4 q^{5} - 4 q^{7} - 16 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(696, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
696.2.y.a	$696$	$2$	696.y	29.d	$7$	$6$	$1$	$5.558$	\(\Q(\zeta_{14})\)	None		✓			696.2.y.a	$2$	$0$	\(0\)	\(1\)	\(-8\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{7}]$	\(q+(1-\zeta_{14}+\zeta_{14}^{2}-\zeta_{14}^{3}+\zeta_{14}^{4}+\cdots)q^{3}+\cdots\)
696.2.y.b	$696$	$2$	696.y	29.d	$7$	$18$	$3$	$5.558$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None		✓			696.2.y.b	$2$	$0$	\(0\)	\(3\)	\(3\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{7}]$	\(q-\beta _{12}q^{3}+(\beta _{1}-\beta _{4}-\beta _{6}-\beta _{10}+\beta _{12}+\cdots)q^{5}+\cdots\)
696.2.y.c	$696$	$2$	696.y	29.d	$7$	$24$	$4$	$5.558$		None		✓			696.2.y.c	$2$	$0$	\(0\)	\(-4\)	\(1\)	\(4\)		$\mathrm{SU}(2)[C_{7}]$
696.2.y.d	$696$	$2$	696.y	29.d	$7$	$24$	$4$	$5.558$		None		✓			696.2.y.d	$2$	$0$	\(0\)	\(-4\)	\(6\)	\(-6\)		$\mathrm{SU}(2)[C_{7}]$
696.2.y.e	$696$	$2$	696.y	29.d	$7$	$24$	$4$	$5.558$		None		✓			696.2.y.e	$2$	$0$	\(0\)	\(4\)	\(2\)	\(-6\)		$\mathrm{SU}(2)[C_{7}]$

Decomposition of \(S_{2}^{\mathrm{old}}(696, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(696, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(29, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(58, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(87, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(116, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(174, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(232, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(348, [\chi])\)\(^{\oplus 2}\)