Space of modular forms of level 952, weight 2, and Character 952.q

• Label: 952.2.q
• Level: $952$
• Weight: $2$
• Character orbit: 952.q
• Rep. character: $\chi_{952}(137,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $64$
• Newform subspaces: $6$
• Sturm bound: $288$
• Trace bound: $3$

Defining parameters

Level:	$N$	$=$	$952 = 2^{3} \cdot 7 \cdot 17$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	952.q (of order $3$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$7$
Character field:			$\Q(\zeta_{3})$
Newform subspaces:			$6$
Sturm bound:			$288$
Trace bound:			$3$
Distinguishing $T_p$:			$3$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(952, [\chi])$.

	Total	New	Old
Modular forms	304	64	240
Cusp forms	272	64	208
Eisenstein series	32	0	32

Trace form

64 * q + 4 * q^3 - 4 * q^5 - 28 * q^9 + 4 * q^11 + 8 * q^13 + 8 * q^15 - 4 * q^17 + 8 * q^21 - 8 * q^23 - 44 * q^25 - 32 * q^27 + 24 * q^29 - 12 * q^31 - 8 * q^33 - 8 * q^35 - 4 * q^37 - 12 * q^39 + 48 * q^41 + 24 * q^43 - 8 * q^45 - 20 * q^49 + 4 * q^53 - 16 * q^55 - 72 * q^57 - 4 * q^59 + 8 * q^61 + 32 * q^63 + 24 * q^65 - 4 * q^67 - 32 * q^69 - 32 * q^71 + 12 * q^73 + 28 * q^75 - 24 * q^77 - 12 * q^79 - 4 * q^81 + 20 * q^87 + 20 * q^89 - 48 * q^91 - 16 * q^93 + 16 * q^95 - 40 * q^99

Decomposition of $S_{2}^{\mathrm{new}}(952, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
952.2.q.a	$952$	$2$	952.q	7.c	$3$	$2$	$1$	$7.602$	$\Q(\sqrt{-3})$	None		✓			952.2.q.a	$2$	$0$	$0$	$0$	$1$	$-5$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{5}+(-3+\zeta_{6})q^{7}+3\zeta_{6}q^{9}+\cdots$
952.2.q.b	$952$	$2$	952.q	7.c	$3$	$2$	$1$	$7.602$	$\Q(\sqrt{-3})$	None		✓			952.2.q.b	$2$	$0$	$0$	$3$	$-2$	$4$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(3-3\zeta_{6})q^{3}-2\zeta_{6}q^{5}+(3-2\zeta_{6})q^{7}+\cdots$
952.2.q.c	$952$	$2$	952.q	7.c	$3$	$12$	$6$	$7.602$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		✓			952.2.q.c	$2$	$0$	$0$	$-1$	$-1$	$3$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{3}-\beta _{11}q^{5}+(\beta _{2}-\beta _{6}-\beta _{9}+\cdots)q^{7}+\cdots$
952.2.q.d	$952$	$2$	952.q	7.c	$3$	$14$	$7$	$7.602$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	None		✓			952.2.q.d	$2$	$0$	$0$	$0$	$1$	$-7$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{3}+(\beta _{3}-\beta _{10})q^{5}+(-\beta _{4}+\beta _{5}+\cdots)q^{7}+\cdots$
952.2.q.e	$952$	$2$	952.q	7.c	$3$	$14$	$7$	$7.602$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None		✓			952.2.q.e	$2$	$0$	$0$	$3$	$-2$	$2$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{3}-\beta _{13}q^{5}+(\beta _{4}-\beta _{7}+\beta _{10}+\cdots)q^{7}+\cdots$
952.2.q.f	$952$	$2$	952.q	7.c	$3$	$20$	$10$	$7.602$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		✓	✓		952.2.q.f	$2$	$0$	$0$	$-1$	$-1$	$3$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{1}+\beta _{2})q^{3}+\beta _{12}q^{5}+\beta _{18}q^{7}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(952, [\chi])$ into lower level spaces

$S_{2}^{\mathrm{old}}(952, [\chi]) \simeq$ $S_{2}^{\mathrm{new}}(28, [\chi])$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(56, [\chi])$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(119, [\chi])$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(238, [\chi])$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(476, [\chi])$$^{\oplus 2}$