Space of modular forms of level 464, weight 2, and Character 464.u

• Label: 464.2.u
• Level: $464$
• Weight: $2$
• Character orbit: 464.u
• Rep. character: $\chi_{464}(49,\cdot)$
• Character field: $\Q(\zeta_{7})$
• Dimension: $84$
• Newform subspaces: $9$
• Sturm bound: $120$
• Trace bound: $5$

Defining parameters

Level:	$N$	$=$	$464 = 2^{4} \cdot 29$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	464.u (of order $7$ and degree $6$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$29$
Character field:			$\Q(\zeta_{7})$
Newform subspaces:			$9$
Sturm bound:			$120$
Trace bound:			$5$
Distinguishing $T_p$:			$3$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(464, [\chi])$.

	Total	New	Old
Modular forms	396	96	300
Cusp forms	324	84	240
Eisenstein series	72	12	60

Trace form

84 * q + 5 * q^3 - 7 * q^5 + 3 * q^7 - 17 * q^9 + 15 * q^11 - 7 * q^13 - q^15 - 10 * q^17 + 5 * q^19 - 7 * q^21 - 5 * q^23 + 7 * q^25 - 13 * q^27 - 7 * q^29 + 5 * q^31 - 7 * q^33 + 7 * q^35 - 7 * q^37 + 53 * q^39 - 10 * q^41 + q^43 + 28 * q^45 + 5 * q^47 - 21 * q^49 + 56 * q^51 + 19 * q^55 - 6 * q^57 - 108 * q^59 - 23 * q^61 + 11 * q^63 + 10 * q^65 + 15 * q^67 - 7 * q^69 + 23 * q^71 - 38 * q^73 + 4 * q^75 + 9 * q^77 + 55 * q^79 + 3 * q^81 + 35 * q^83 - 42 * q^85 - 71 * q^87 + 5 * q^89 - 9 * q^91 - 59 * q^93 + 55 * q^95 - 10 * q^97 - 140 * q^99

Decomposition of $S_{2}^{\mathrm{new}}(464, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
464.2.u.a	$464$	$2$	464.u	29.d	$7$	$6$	$1$	$3.705$	$\Q(\zeta_{14})$	None					232.2.m.c	$2$	$0$	$0$	$-5$	$7$	$3$	$1$	$\mathrm{SU}(2)[C_{7}]$	$q+(-1+\zeta_{14}^{5})q^{3}+(1-\zeta_{14}-2\zeta_{14}^{4}+\cdots)q^{5}+\cdots$
464.2.u.b	$464$	$2$	464.u	29.d	$7$	$6$	$1$	$3.705$	$\Q(\zeta_{14})$	None					58.2.d.a	$2$	$0$	$0$	$-3$	$-4$	$5$	$1$	$\mathrm{SU}(2)[C_{7}]$	$q+(-1+\zeta_{14}-\zeta_{14}^{4}+\zeta_{14}^{5})q^{3}+\cdots$
464.2.u.c	$464$	$2$	464.u	29.d	$7$	$6$	$1$	$3.705$	$\Q(\zeta_{14})$	None					116.2.g.a	$2$	$0$	$0$	$-3$	$-3$	$-3$	$1$	$\mathrm{SU}(2)[C_{7}]$	$q+(1-2\zeta_{14}+2\zeta_{14}^{2}-2\zeta_{14}^{3}+2\zeta_{14}^{4}+\cdots)q^{3}+\cdots$
464.2.u.d	$464$	$2$	464.u	29.d	$7$	$6$	$1$	$3.705$	$\Q(\zeta_{14})$	None					232.2.m.b	$2$	$0$	$0$	$1$	$-1$	$-5$	$1$	$\mathrm{SU}(2)[C_{7}]$	$q+(1+2\zeta_{14}^{2}-2\zeta_{14}^{3}-\zeta_{14}^{5})q^{3}+\cdots$
464.2.u.e	$464$	$2$	464.u	29.d	$7$	$6$	$1$	$3.705$	$\Q(\zeta_{14})$	None					232.2.m.a	$2$	$0$	$0$	$3$	$2$	$3$	$1$	$\mathrm{SU}(2)[C_{7}]$	$q+(1-\zeta_{14}+\zeta_{14}^{4}-\zeta_{14}^{5})q^{3}+(\zeta_{14}^{3}+\cdots)q^{5}+\cdots$
464.2.u.f	$464$	$2$	464.u	29.d	$7$	$6$	$1$	$3.705$	$\Q(\zeta_{14})$	None					29.2.d.a	$2$	$0$	$0$	$5$	$1$	$-1$	$1$	$\mathrm{SU}(2)[C_{7}]$	$q+(1-\zeta_{14}^{5})q^{3}+(1-\zeta_{14}-2\zeta_{14}^{3}+\cdots)q^{5}+\cdots$
464.2.u.g	$464$	$2$	464.u	29.d	$7$	$12$	$2$	$3.705$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None					116.2.g.b	$2$	$0$	$0$	$3$	$-1$	$7$	$1$	$\mathrm{SU}(2)[C_{7}]$	$q+(\beta _{1}+\beta _{8})q^{3}+(-\beta _{2}+\beta _{3}+\beta _{4}+\beta _{5}+\cdots)q^{5}+\cdots$
464.2.u.h	$464$	$2$	464.u	29.d	$7$	$12$	$2$	$3.705$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None					58.2.d.b	$2$	$0$	$0$	$3$	$0$	$-1$	$1$	$\mathrm{SU}(2)[C_{7}]$	$q-\beta _{11}q^{3}+(\beta _{1}+\beta _{3}-\beta _{4}+\beta _{5}-\beta _{7}+\cdots)q^{5}+\cdots$
464.2.u.i	$464$	$2$	464.u	29.d	$7$	$24$	$4$	$3.705$		None			✓		232.2.m.d	$2$	$0$	$0$	$1$	$-8$	$-5$		$\mathrm{SU}(2)[C_{7}]$

Decomposition of $S_{2}^{\mathrm{old}}(464, [\chi])$ into lower level spaces

$S_{2}^{\mathrm{old}}(464, [\chi]) \simeq$ $S_{2}^{\mathrm{new}}(29, [\chi])$$^{\oplus 5}$$\oplus$$S_{2}^{\mathrm{new}}(58, [\chi])$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(116, [\chi])$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(232, [\chi])$$^{\oplus 2}$