Space of modular forms of level 700, weight 2, and Character 700.p

• Label: 700.2.p
• Level: $700$
• Weight: $2$
• Character orbit: 700.p
• Rep. character: $\chi_{700}(451,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $140$
• Newform subspaces: $6$
• Sturm bound: $240$
• Trace bound: $2$

Defining parameters

Level:	$N$	$=$	$700 = 2^{2} \cdot 5^{2} \cdot 7$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	700.p (of order $6$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$28$
Character field:			$\Q(\zeta_{6})$
Newform subspaces:			$6$
Sturm bound:			$240$
Trace bound:			$2$
Distinguishing $T_p$:			$3$, $17$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(700, [\chi])$.

	Total	New	Old
Modular forms	264	164	100
Cusp forms	216	140	76
Eisenstein series	48	24	24

Trace form

140 * q + 2 * q^4 + 12 * q^8 - 56 * q^9 + 18 * q^12 - 20 * q^14 - 2 * q^16 + 6 * q^17 - 6 * q^21 + 12 * q^22 + 12 * q^24 - 30 * q^26 + 18 * q^28 + 16 * q^29 - 10 * q^32 - 6 * q^33 - 44 * q^36 - 2 * q^37 + 42 * q^38 + 50 * q^42 + 36 * q^44 - 22 * q^46 + 28 * q^49 + 36 * q^52 + 6 * q^53 + 24 * q^54 - 42 * q^56 - 12 * q^57 + 6 * q^58 - 30 * q^61 - 16 * q^64 - 138 * q^66 - 60 * q^68 - 4 * q^72 + 42 * q^73 + 16 * q^74 + 50 * q^77 - 144 * q^78 - 34 * q^81 - 54 * q^82 + 98 * q^84 + 4 * q^86 - 8 * q^88 - 54 * q^89 - 4 * q^92 + 2 * q^93 + 48 * q^94 + 114 * q^96 - 56 * q^98

Decomposition of $S_{2}^{\mathrm{new}}(700, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
700.2.p.a	$700$	$2$	700.p	28.f	$6$	$4$	$2$	$5.590$	$\Q(\zeta_{12})$	None					28.2.f.a	$4$	$0$	$2$	$0$	$0$	$0$	$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\cdots)q^{3}+\cdots$
700.2.p.b	$700$	$2$	700.p	28.f	$6$	$8$	$4$	$5.590$	8.0.3317760000.8	$\Q(\sqrt{-5})$					140.2.s.a	$8$	$0$	$0$	$0$	$0$	$0$	$1$	$\mathrm{U}(1)[D_{6}]$	$q+\beta _{5}q^{2}+(\beta _{1}+\beta _{5})q^{3}+2\beta _{3}q^{4}+(-1+\cdots)q^{6}+\cdots$
700.2.p.c	$700$	$2$	700.p	28.f	$6$	$32$	$16$	$5.590$		None					140.2.o.a	$4$	$0$	$-2$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{6}]$
700.2.p.d	$700$	$2$	700.p	28.f	$6$	$32$	$16$	$5.590$		None		✓			700.2.p.d	$4$	$0$	$-1$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{6}]$
700.2.p.e	$700$	$2$	700.p	28.f	$6$	$32$	$16$	$5.590$		None					140.2.s.b	$8$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{6}]$
700.2.p.f	$700$	$2$	700.p	28.f	$6$	$32$	$16$	$5.590$		None		✓			700.2.p.d	$4$	$0$	$1$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{6}]$

Decomposition of $S_{2}^{\mathrm{old}}(700, [\chi])$ into lower level spaces

$S_{2}^{\mathrm{old}}(700, [\chi]) \simeq$ $S_{2}^{\mathrm{new}}(28, [\chi])$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(140, [\chi])$$^{\oplus 2}$