Space of modular forms of level 529, weight 2, and Character 529.c

• Label: 529.2.c
• Level: $529$
• Weight: $2$
• Character orbit: 529.c
• Rep. character: $\chi_{529}(118,\cdot)$
• Character field: $\Q(\zeta_{11})$
• Dimension: $320$
• Newform subspaces: $18$
• Sturm bound: $92$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 529 = 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	529.c (of order \(11\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 23 \)
Character field:			\(\Q(\zeta_{11})\)
Newform subspaces:			\( 18 \)
Sturm bound:			\(92\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(2\), \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(529, [\chi])\).

	Total	New	Old
Modular forms	580	520	60
Cusp forms	340	320	20
Eisenstein series	240	200	40

Trace form

320 * q + 7 * q^2 + 7 * q^3 - 19 * q^4 + 3 * q^5 - 9 * q^6 + 5 * q^7 - 7 * q^8 - 9 * q^9 - q^10 - 7 * q^11 - 15 * q^12 + 3 * q^13 - 9 * q^14 - 12 * q^15 - q^16 + 10 * q^17 + 11 * q^18 - 2 * q^19 + 9 * q^20 + 2 * q^21 + 6 * q^22 - 122 * q^24 + 15 * q^25 - 15 * q^26 - 2 * q^27 - 7 * q^28 - 16 * q^29 - 7 * q^30 - 12 * q^31 - 27 * q^32 - 16 * q^33 - 29 * q^34 - 9 * q^35 - 8 * q^36 + 19 * q^37 + 8 * q^38 - 7 * q^39 - q^40 - 9 * q^41 + 25 * q^42 + 11 * q^43 + 34 * q^44 + 6 * q^45 - 162 * q^47 - 27 * q^48 + 49 * q^49 + 24 * q^50 - 7 * q^51 + 11 * q^52 - 29 * q^53 - 3 * q^54 - 3 * q^55 + 2 * q^56 + 8 * q^57 + 14 * q^58 + 13 * q^59 - 25 * q^60 - 3 * q^61 - 11 * q^62 - 34 * q^63 + 11 * q^64 - 2 * q^65 - 2 * q^66 - 45 * q^67 + 30 * q^68 - 178 * q^70 + 8 * q^71 - 34 * q^72 - 27 * q^73 - 10 * q^74 + 20 * q^75 + 16 * q^76 - 10 * q^77 + 59 * q^78 + 15 * q^79 + 52 * q^80 + 91 * q^81 - 29 * q^82 - 18 * q^83 + 17 * q^84 + 9 * q^85 + 11 * q^86 + 9 * q^87 - 27 * q^88 - 25 * q^89 + 20 * q^90 + 4 * q^91 - 104 * q^93 - 34 * q^94 - 18 * q^95 + 80 * q^96 + 34 * q^97 - 31 * q^98 + 30 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(529, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
529.2.c.a	$529$	$2$	529.c	23.c	$11$	$10$	$1$	$4.224$	\(\Q(\zeta_{22})\)	None					23.2.c.a	$2$	$0$	\(-7\)	\(-7\)	\(3\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{11}]$	\(q+(-1+\zeta_{22}+\zeta_{22}^{7}-\zeta_{22}^{8})q^{2}+\cdots\)
529.2.c.b	$529$	$2$	529.c	23.c	$11$	$10$	$1$	$4.224$	\(\Q(\zeta_{22})\)	None					23.2.c.a	$2$	$0$	\(-7\)	\(4\)	\(-3\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{11}]$	\(q+(-1-\zeta_{22}^{2}-\zeta_{22}^{6}-\zeta_{22}^{8})q^{2}+\cdots\)
529.2.c.c	$529$	$2$	529.c	23.c	$11$	$10$	$1$	$4.224$	\(\Q(\zeta_{22})\)	None					23.2.c.a	$2$	$0$	\(-7\)	\(4\)	\(3\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{11}]$	\(q+(-1-\zeta_{22}^{2}-\zeta_{22}^{6}-\zeta_{22}^{8})q^{2}+\cdots\)
529.2.c.d	$529$	$2$	529.c	23.c	$11$	$10$	$1$	$4.224$	\(\Q(\zeta_{22})\)	None					23.2.c.a	$2$	$0$	\(4\)	\(-7\)	\(-3\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{11}]$	\(q+(1+\zeta_{22}^{2}-\zeta_{22}^{3}+\zeta_{22}^{4}-\zeta_{22}^{5}+\cdots)q^{2}+\cdots\)
529.2.c.e	$529$	$2$	529.c	23.c	$11$	$10$	$1$	$4.224$	\(\Q(\zeta_{22})\)	None					23.2.c.a	$2$	$0$	\(4\)	\(-7\)	\(3\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{11}]$	\(q+(1+\zeta_{22}^{2}-\zeta_{22}^{3}+\zeta_{22}^{4}-\zeta_{22}^{5}+\cdots)q^{2}+\cdots\)
529.2.c.f	$529$	$2$	529.c	23.c	$11$	$10$	$1$	$4.224$	\(\Q(\zeta_{22})\)	None					23.2.c.a	$2$	$0$	\(4\)	\(4\)	\(-8\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{11}]$	\(q+(1-\zeta_{22}+\zeta_{22}^{2}+\zeta_{22}^{4}+\zeta_{22}^{6}+\cdots)q^{2}+\cdots\)
529.2.c.g	$529$	$2$	529.c	23.c	$11$	$10$	$1$	$4.224$	\(\Q(\zeta_{22})\)	None					23.2.c.a	$2$	$0$	\(4\)	\(4\)	\(8\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{11}]$	\(q+(1-\zeta_{22}+\zeta_{22}^{2}+\zeta_{22}^{4}+\zeta_{22}^{6}+\cdots)q^{2}+\cdots\)
529.2.c.h	$529$	$2$	529.c	23.c	$11$	$10$	$1$	$4.224$	\(\Q(\zeta_{22})\)	None					23.2.c.a	$2$	$0$	\(4\)	\(4\)	\(-8\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{11}]$	\(q+(-\zeta_{22}^{2}+\zeta_{22}^{3}+\zeta_{22}^{5}-\zeta_{22}^{6}+\cdots)q^{2}+\cdots\)
529.2.c.i	$529$	$2$	529.c	23.c	$11$	$10$	$1$	$4.224$	\(\Q(\zeta_{22})\)	None					23.2.c.a	$2$	$0$	\(4\)	\(4\)	\(8\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{11}]$	\(q+(-\zeta_{22}^{2}+\zeta_{22}^{3}+\zeta_{22}^{5}-\zeta_{22}^{6}+\cdots)q^{2}+\cdots\)
529.2.c.j	$529$	$2$	529.c	23.c	$11$	$20$	$2$	$4.224$	20.0.\(\cdots\).6	None		✓			529.2.a.d	$10$	$0$	\(-2\)	\(0\)	\(-2\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{11}]$	\(q+(\beta _{5}+\beta _{16})q^{2}+\beta _{7}q^{3}+(-2\beta _{1}-2\beta _{3}+\cdots)q^{4}+\cdots\)
529.2.c.k	$529$	$2$	529.c	23.c	$11$	$20$	$2$	$4.224$	20.0.\(\cdots\).6	None		✓			529.2.a.d	$10$	$0$	\(-2\)	\(0\)	\(2\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{11}]$	\(q+(\beta _{5}+\beta _{16})q^{2}+\beta _{7}q^{3}+(-2\beta _{1}-2\beta _{3}+\cdots)q^{4}+\cdots\)
529.2.c.l	$529$	$2$	529.c	23.c	$11$	$20$	$2$	$4.224$	20.0.\(\cdots\).3	None		✓			529.2.a.b	$10$	$0$	\(0\)	\(-2\)	\(0\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{11}]$	\(q+\beta _{9}q^{2}+(\beta _{6}+\beta _{17})q^{3}+\beta _{18}q^{4}+\cdots\)
529.2.c.m	$529$	$2$	529.c	23.c	$11$	$20$	$2$	$4.224$	20.0.\(\cdots\).3	None		✓			529.2.a.b	$10$	$0$	\(0\)	\(-2\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{11}]$	\(q+\beta _{9}q^{2}+(\beta _{6}+\beta _{17})q^{3}+\beta _{18}q^{4}+\cdots\)
529.2.c.n	$529$	$2$	529.c	23.c	$11$	$20$	$2$	$4.224$	20.0.\(\cdots\).1	None					23.2.a.a	$10$	$0$	\(1\)	\(0\)	\(-2\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{11}]$	\(q+\beta _{16}q^{2}+(1+2\beta _{1}+2\beta _{2}+\beta _{3}-2\beta _{4}+\cdots)q^{3}+\cdots\)
529.2.c.o	$529$	$2$	529.c	23.c	$11$	$20$	$2$	$4.224$	20.0.\(\cdots\).1	None					23.2.a.a	$10$	$0$	\(1\)	\(0\)	\(2\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{11}]$	\(q+\beta _{16}q^{2}+(1+2\beta _{1}+2\beta _{2}+\beta _{3}-2\beta _{4}+\cdots)q^{3}+\cdots\)
529.2.c.p	$529$	$2$	529.c	23.c	$11$	$30$	$3$	$4.224$		\(\Q(\sqrt{-23}) \)		✓			529.2.a.f	$20$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{U}(1)[D_{11}]$
529.2.c.q	$529$	$2$	529.c	23.c	$11$	$40$	$4$	$4.224$		None		✓			529.2.a.h	$20$	$0$	\(2\)	\(4\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{11}]$
529.2.c.r	$529$	$2$	529.c	23.c	$11$	$40$	$4$	$4.224$		None		✓			529.2.a.g	$20$	$0$	\(4\)	\(4\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{11}]$

Decomposition of \(S_{2}^{\mathrm{old}}(529, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(529, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 2}\)