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

• Label: 464.2.y
• Level: $464$
• Weight: $2$
• Character orbit: 464.y
• Rep. character: $\chi_{464}(33,\cdot)$
• Character field: $\Q(\zeta_{14})$
• Dimension: $84$
• Newform subspaces: $5$
• Sturm bound: $120$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 464 = 2^{4} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	464.y (of order \(14\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 29 \)
Character field:			\(\Q(\zeta_{14})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(120\)
Trace bound:			\(3\)
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 + 7 * q^3 - 7 * q^5 + 7 * q^7 + 7 * q^9 - 7 * q^11 - 3 * q^13 + 7 * q^15 + 7 * q^19 - 7 * q^21 + 15 * q^23 - 33 * q^25 + 7 * q^27 - 13 * q^29 + 7 * q^31 - 3 * q^33 + 7 * q^35 - 7 * q^37 - 35 * q^39 + 7 * q^43 - 18 * q^45 + 7 * q^47 - 21 * q^49 + 26 * q^51 - 10 * q^53 + 7 * q^55 - 18 * q^57 + 132 * q^59 - 7 * q^61 - 49 * q^63 + 7 * q^67 - 7 * q^69 - 25 * q^71 + 28 * q^73 - 7 * q^77 - 63 * q^79 - 9 * q^81 - 25 * q^83 + 28 * q^85 + 107 * q^87 - 7 * q^89 + 15 * q^91 + 49 * q^93 + 7 * q^95 - 14 * q^97

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.y.a	$464$	$2$	464.y	29.e	$14$	$6$	$1$	$3.705$	\(\Q(\zeta_{14})\)	None					116.2.i.b	$2$	$0$	\(0\)	\(-7\)	\(-1\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{14}]$	\(q+(-1-\zeta_{14}^{3})q^{3}+(1-2\zeta_{14}+\zeta_{14}^{2}+\cdots)q^{5}+\cdots\)
464.2.y.b	$464$	$2$	464.y	29.e	$14$	$6$	$1$	$3.705$	\(\Q(\zeta_{14})\)	None					116.2.i.a	$2$	$0$	\(0\)	\(7\)	\(-1\)	\(-9\)	$1$	$\mathrm{SU}(2)[C_{14}]$	\(q+(1+\zeta_{14}^{3})q^{3}+(-1-\zeta_{14}^{2}-2\zeta_{14}^{4}+\cdots)q^{5}+\cdots\)
464.2.y.c	$464$	$2$	464.y	29.e	$14$	$12$	$2$	$3.705$	\(\Q(\zeta_{28})\)	None					58.2.e.a	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{14}]$	\(q+(\zeta_{28}-\zeta_{28}^{5}+\zeta_{28}^{11})q^{3}+(2\zeta_{28}+\cdots)q^{5}+\cdots\)
464.2.y.d	$464$	$2$	464.y	29.e	$14$	$12$	$2$	$3.705$	12.0.\(\cdots\).1	None					29.2.e.a	$2$	$0$	\(0\)	\(7\)	\(-1\)	\(11\)	$1$	$\mathrm{SU}(2)[C_{14}]$	\(q+(2+\beta _{1}+\beta _{5}+\beta _{7}+\beta _{8}-\beta _{9})q^{3}+\cdots\)
464.2.y.e	$464$	$2$	464.y	29.e	$14$	$48$	$8$	$3.705$		None			✓		232.2.q.a	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(4\)		$\mathrm{SU}(2)[C_{14}]$

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

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