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

\( 84 q + 5 q^{3} - 7 q^{5} + 3 q^{7} - 17 q^{9} + O(q^{10}) \)

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	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		$2$	$0$	\(0\)	\(-5\)	\(7\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{7}]$	\(q+(-1+\zeta_{14}^{5})q^{3}+(1-\zeta_{14}-2\zeta_{14}^{4}+\cdots)q^{5}+\cdots\)
464.2.u.b	$464$	$2$	464.u	29.d	$7$	$6$	$1$	$3.705$	\(\Q(\zeta_{14})\)	None		$2$	$0$	\(0\)	\(-3\)	\(-4\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{7}]$	\(q+(-1+\zeta_{14}-\zeta_{14}^{4}+\zeta_{14}^{5})q^{3}+\cdots\)
464.2.u.c	$464$	$2$	464.u	29.d	$7$	$6$	$1$	$3.705$	\(\Q(\zeta_{14})\)	None		$2$	$0$	\(0\)	\(-3\)	\(-3\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{7}]$	\(q+(1-2\zeta_{14}+2\zeta_{14}^{2}-2\zeta_{14}^{3}+2\zeta_{14}^{4}+\cdots)q^{3}+\cdots\)
464.2.u.d	$464$	$2$	464.u	29.d	$7$	$6$	$1$	$3.705$	\(\Q(\zeta_{14})\)	None		$2$	$0$	\(0\)	\(1\)	\(-1\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{7}]$	\(q+(1+2\zeta_{14}^{2}-2\zeta_{14}^{3}-\zeta_{14}^{5})q^{3}+\cdots\)
464.2.u.e	$464$	$2$	464.u	29.d	$7$	$6$	$1$	$3.705$	\(\Q(\zeta_{14})\)	None		$2$	$0$	\(0\)	\(3\)	\(2\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{7}]$	\(q+(1-\zeta_{14}+\zeta_{14}^{4}-\zeta_{14}^{5})q^{3}+(\zeta_{14}^{3}+\cdots)q^{5}+\cdots\)
464.2.u.f	$464$	$2$	464.u	29.d	$7$	$6$	$1$	$3.705$	\(\Q(\zeta_{14})\)	None		$2$	$0$	\(0\)	\(5\)	\(1\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{7}]$	\(q+(1-\zeta_{14}^{5})q^{3}+(1-\zeta_{14}-2\zeta_{14}^{3}+\cdots)q^{5}+\cdots\)
464.2.u.g	$464$	$2$	464.u	29.d	$7$	$12$	$2$	$3.705$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(0\)	\(3\)	\(-1\)	\(7\)	$1$	$\mathrm{SU}(2)[C_{7}]$	\(q+(\beta _{1}+\beta _{8})q^{3}+(-\beta _{2}+\beta _{3}+\beta _{4}+\beta _{5}+\cdots)q^{5}+\cdots\)
464.2.u.h	$464$	$2$	464.u	29.d	$7$	$12$	$2$	$3.705$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(0\)	\(3\)	\(0\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{7}]$	\(q-\beta _{11}q^{3}+(\beta _{1}+\beta _{3}-\beta _{4}+\beta _{5}-\beta _{7}+\cdots)q^{5}+\cdots\)
464.2.u.i	$464$	$2$	464.u	29.d	$7$	$24$	$4$	$3.705$		None		$2$	$0$	\(0\)	\(1\)	\(-8\)	\(-5\)		$\mathrm{SU}(2)[C_{7}]$

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

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