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

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