Space of modular forms of level 2142, weight 2, and Character 2142.p

• Label: 2142.2.p
• Level: $2142$
• Weight: $2$
• Character orbit: 2142.p
• Rep. character: $\chi_{2142}(1135,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $88$
• Newform subspaces: $9$
• Sturm bound: $864$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 2142 = 2 \cdot 3^{2} \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2142.p (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(864\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2142, [\chi])\).

	Total	New	Old
Modular forms	896	88	808
Cusp forms	832	88	744
Eisenstein series	64	0	64

Trace form

88 * q - 88 * q^4 + 4 * q^5 - 4 * q^10 + 4 * q^11 - 32 * q^13 + 88 * q^16 - 4 * q^17 - 4 * q^20 + 4 * q^22 - 28 * q^29 + 40 * q^31 + 28 * q^34 + 8 * q^35 - 12 * q^37 + 8 * q^38 + 4 * q^40 - 40 * q^41 - 4 * q^44 + 80 * q^47 + 48 * q^50 + 32 * q^52 - 32 * q^55 + 12 * q^58 - 4 * q^61 + 24 * q^62 - 88 * q^64 - 48 * q^65 - 72 * q^67 + 4 * q^68 + 24 * q^71 + 32 * q^73 - 4 * q^74 + 24 * q^79 + 4 * q^80 - 40 * q^82 - 12 * q^85 - 8 * q^86 - 4 * q^88 + 32 * q^89 - 16 * q^91 + 88 * q^95 + 72 * q^97 - 8 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(2142, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2142.2.p.a	$2142$	$2$	2142.p	17.c	$4$	$4$	$2$	$17.104$	\(\Q(\zeta_{8})\)	None					714.2.m.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\zeta_{8}^{2}q^{2}-q^{4}+\zeta_{8}q^{5}-\zeta_{8}^{3}q^{7}+\cdots\)
2142.2.p.b	$2142$	$2$	2142.p	17.c	$4$	$4$	$2$	$17.104$	\(\Q(\zeta_{8})\)	None					714.2.m.a	$2$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-\zeta_{8}^{2}q^{2}-q^{4}+(2+\zeta_{8}+2\zeta_{8}^{2})q^{5}+\cdots\)
2142.2.p.c	$2142$	$2$	2142.p	17.c	$4$	$8$	$4$	$17.104$	\(\Q(\zeta_{16})\)	None					238.2.g.a	$2$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta_{3} q^{2}-q^{4}+(\beta_{7}-\beta_{3}-1)q^{5}+\cdots\)
2142.2.p.d	$2142$	$2$	2142.p	17.c	$4$	$8$	$4$	$17.104$	8.0.836829184.2	None					714.2.m.c	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{5}q^{2}-q^{4}+(-\beta _{1}+\beta _{4}-\beta _{5}+\beta _{6}+\cdots)q^{5}+\cdots\)
2142.2.p.e	$2142$	$2$	2142.p	17.c	$4$	$8$	$4$	$17.104$	8.0.110166016.2	None					238.2.g.b	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{5}q^{2}-q^{4}+(-\beta _{2}+\beta _{4}+\beta _{5})q^{5}+\cdots\)
2142.2.p.f	$2142$	$2$	2142.p	17.c	$4$	$12$	$6$	$17.104$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None					714.2.m.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{9}q^{2}-q^{4}+(-\beta _{6}-\beta _{8})q^{5}+\beta _{5}q^{7}+\cdots\)
2142.2.p.g	$2142$	$2$	2142.p	17.c	$4$	$12$	$6$	$17.104$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None					714.2.m.d	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{7}q^{2}-q^{4}-\beta _{6}q^{5}-\beta _{3}q^{7}+\beta _{7}q^{8}+\cdots\)
2142.2.p.h	$2142$	$2$	2142.p	17.c	$4$	$16$	$8$	$17.104$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			2142.2.p.h	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{12}q^{2}-q^{4}-\beta _{5}q^{5}-\beta _{9}q^{7}-\beta _{12}q^{8}+\cdots\)
2142.2.p.i	$2142$	$2$	2142.p	17.c	$4$	$16$	$8$	$17.104$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			2142.2.p.h	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{12}q^{2}-q^{4}+\beta _{5}q^{5}-\beta _{9}q^{7}+\beta _{12}q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2142, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2142, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(51, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(102, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(119, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(153, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(238, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(306, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(357, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(714, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1071, [\chi])\)\(^{\oplus 2}\)