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 + 10 * q^15 - 4 * q^17 - 8 * q^23 - 46 * q^25 - 6 * q^29 - 20 * q^31 + 8 * q^33 + 40 * q^35 - 4 * q^37 - 8 * q^39 - 4 * q^41 - 24 * q^43 - 10 * q^45 + 20 * q^47 + 32 * q^51 + 54 * q^53 + 50 * q^55 + 24 * q^57 + 8 * q^59 + 40 * q^61 + 10 * q^63 + 34 * q^65 + 52 * q^67 + 20 * q^69 + 44 * q^71 - 6 * q^73 + 44 * q^77 - 20 * q^79 - 16 * q^81 + 44 * q^83 - 8 * q^85 - 78 * q^87 + 20 * q^89 - 12 * q^93 + 16 * q^95 + 10 * q^97

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}$