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

• Label: 700.2.be
• Level: $700$
• Weight: $2$
• Character orbit: 700.be
• Rep. character: $\chi_{700}(107,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $272$
• Newform subspaces: $6$
• Sturm bound: $240$
• Trace bound: $3$

Defining parameters

Level:	$N$	$=$	$700 = 2^{2} \cdot 5^{2} \cdot 7$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	700.be (of order $12$ and degree $4$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$140$
Character field:			$\Q(\zeta_{12})$
Newform subspaces:			$6$
Sturm bound:			$240$
Trace bound:			$3$
Distinguishing $T_p$:			$3$

Dimensions

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

	Total	New	Old
Modular forms	528	304	224
Cusp forms	432	272	160
Eisenstein series	96	32	64

Trace form

272 * q + 2 * q^2 - 16 * q^6 + 20 * q^8 - 10 * q^12 + 16 * q^13 + 12 * q^16 + 4 * q^17 + 4 * q^18 + 16 * q^22 - 36 * q^26 - 42 * q^28 + 22 * q^32 + 36 * q^33 - 48 * q^36 + 4 * q^37 - 12 * q^38 - 64 * q^41 - 50 * q^42 - 16 * q^46 - 12 * q^48 - 64 * q^52 + 4 * q^53 - 96 * q^56 - 40 * q^57 - 42 * q^58 - 8 * q^61 - 56 * q^62 - 140 * q^66 - 4 * q^68 - 76 * q^72 + 20 * q^73 - 176 * q^76 + 12 * q^77 - 64 * q^78 + 144 * q^81 + 46 * q^82 - 80 * q^86 - 16 * q^88 - 44 * q^92 + 44 * q^93 + 84 * q^96 + 96 * q^97 + 118 * 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.be.a	$700$	$2$	700.be	140.w	$12$	$8$	$2$	$5.590$	8.0.12960000.1	$\Q(\sqrt{-5})$		✓			700.2.be.a	$8$	$0$	$-4$	$2$	$0$	$6$	$2^{2}$	$\mathrm{U}(1)[D_{12}]$	$q+(\beta _{1}-\beta _{4})q^{2}+(-\beta _{1}-\beta _{2}-\beta _{5})q^{3}+\cdots$
700.2.be.b	$700$	$2$	700.be	140.w	$12$	$8$	$2$	$5.590$	8.0.12960000.1	$\Q(\sqrt{-5})$		✓			700.2.be.a	$8$	$0$	$4$	$-2$	$0$	$-6$	$2^{2}$	$\mathrm{U}(1)[D_{12}]$	$q+(1-\beta _{4}-\beta _{7})q^{2}+(-1-\beta _{3}+2\beta _{6}+\cdots)q^{3}+\cdots$
700.2.be.c	$700$	$2$	700.be	140.w	$12$	$8$	$2$	$5.590$	8.0.$\cdots$.9	None					140.2.w.a	$8$	$0$	$4$	$0$	$0$	$0$	$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(1-\beta _{2}-\beta _{4})q^{2}-\beta _{1}q^{3}+(-2\beta _{2}+\cdots)q^{4}+\cdots$
700.2.be.d	$700$	$2$	700.be	140.w	$12$	$48$	$12$	$5.590$		None		✓			700.2.be.d	$16$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{12}]$
700.2.be.e	$700$	$2$	700.be	140.w	$12$	$72$	$18$	$5.590$		None					140.2.w.b	$8$	$0$	$-2$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{12}]$
700.2.be.f	$700$	$2$	700.be	140.w	$12$	$128$	$32$	$5.590$		None		✓	✓		700.2.be.f	$16$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{12}]$

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

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