Space of modular forms of level 968, weight 2, and Character 968.i

• Label: 968.2.i
• Level: $968$
• Weight: $2$
• Character orbit: 968.i
• Rep. character: $\chi_{968}(9,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $108$
• Newform subspaces: $20$
• Sturm bound: $264$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 968 = 2^{3} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	968.i (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 20 \)
Sturm bound:			\(264\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(968, [\chi])\).

	Total	New	Old
Modular forms	624	108	516
Cusp forms	432	108	324
Eisenstein series	192	0	192

Trace form

108 * q - 2 * q^3 - 4 * q^7 - 21 * q^9 - 2 * q^13 + 18 * q^15 + 8 * q^17 + 11 * q^19 + 8 * q^21 + 28 * q^23 - 3 * q^25 + 19 * q^27 - 6 * q^31 - 10 * q^35 - 16 * q^37 - 44 * q^39 - 20 * q^41 - 30 * q^43 - 76 * q^45 - 18 * q^47 - 45 * q^49 - 35 * q^51 + 36 * q^53 + 9 * q^57 + 29 * q^59 + 18 * q^61 + 8 * q^63 + 20 * q^65 + 82 * q^67 + 52 * q^69 + 36 * q^71 + 8 * q^73 - 3 * q^75 + 8 * q^79 - 68 * q^81 + 13 * q^83 - 36 * q^85 + 40 * q^87 - 46 * q^89 - 30 * q^91 - 6 * q^93 - 4 * q^95 + 7 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(968, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
968.2.i.a	$968$	$2$	968.i	11.c	$5$	$4$	$1$	$7.730$	\(\Q(\zeta_{10})\)	None		✓			968.2.a.f	$2$	$0$	\(0\)	\(-4\)	\(-5\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-2\zeta_{10}-2\zeta_{10}^{3})q^{3}+(-2+\zeta_{10}+\cdots)q^{5}+\cdots\)
968.2.i.b	$968$	$2$	968.i	11.c	$5$	$4$	$1$	$7.730$	\(\Q(\zeta_{10})\)	None		✓			968.2.a.f	$2$	$0$	\(0\)	\(-4\)	\(-5\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-2\zeta_{10}-2\zeta_{10}^{3})q^{3}+(-2+\zeta_{10}+\cdots)q^{5}+\cdots\)
968.2.i.c	$968$	$2$	968.i	11.c	$5$	$4$	$1$	$7.730$	\(\Q(\zeta_{10})\)	None					88.2.i.a	$2$	$1$	\(0\)	\(-2\)	\(-2\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-\zeta_{10}-\zeta_{10}^{3})q^{3}+(-1+\zeta_{10}+\cdots)q^{5}+\cdots\)
968.2.i.d	$968$	$2$	968.i	11.c	$5$	$4$	$1$	$7.730$	\(\Q(\zeta_{10})\)	None					88.2.i.a	$2$	$0$	\(0\)	\(-2\)	\(-2\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-\zeta_{10}-\zeta_{10}^{3})q^{3}+(-1+\zeta_{10}+\cdots)q^{5}+\cdots\)
968.2.i.e	$968$	$2$	968.i	11.c	$5$	$4$	$1$	$7.730$	\(\Q(\zeta_{10})\)	None		✓			968.2.a.d	$4$	$0$	\(0\)	\(-1\)	\(-1\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+\zeta_{10}^{2}q^{3}-\zeta_{10}q^{5}-4\zeta_{10}^{3}q^{7}+\cdots\)
968.2.i.f	$968$	$2$	968.i	11.c	$5$	$4$	$1$	$7.730$	\(\Q(\zeta_{10})\)	None		✓			968.2.a.d	$4$	$0$	\(0\)	\(-1\)	\(-1\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+\zeta_{10}^{2}q^{3}-\zeta_{10}q^{5}+4\zeta_{10}^{3}q^{7}+\cdots\)
968.2.i.g	$968$	$2$	968.i	11.c	$5$	$4$	$1$	$7.730$	\(\Q(\zeta_{10})\)	None		✓			968.2.a.b	$4$	$0$	\(0\)	\(0\)	\(-3\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q-3\zeta_{10}q^{5}-4\zeta_{10}^{3}q^{7}+(3-3\zeta_{10}+\cdots)q^{9}+\cdots\)
968.2.i.h	$968$	$2$	968.i	11.c	$5$	$4$	$1$	$7.730$	\(\Q(\zeta_{10})\)	None		✓			968.2.a.b	$4$	$0$	\(0\)	\(0\)	\(-3\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q-3\zeta_{10}q^{5}+4\zeta_{10}^{3}q^{7}+(3-3\zeta_{10}+\cdots)q^{9}+\cdots\)
968.2.i.i	$968$	$2$	968.i	11.c	$5$	$4$	$1$	$7.730$	\(\Q(\zeta_{10})\)	None					88.2.a.a	$4$	$0$	\(0\)	\(3\)	\(3\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q-3\zeta_{10}^{2}q^{3}+3\zeta_{10}q^{5}-2\zeta_{10}^{3}q^{7}+\cdots\)
968.2.i.j	$968$	$2$	968.i	11.c	$5$	$4$	$1$	$7.730$	\(\Q(\zeta_{10})\)	None					88.2.a.a	$4$	$0$	\(0\)	\(3\)	\(3\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q-3\zeta_{10}^{2}q^{3}+3\zeta_{10}q^{5}+2\zeta_{10}^{3}q^{7}+\cdots\)
968.2.i.k	$968$	$2$	968.i	11.c	$5$	$4$	$1$	$7.730$	\(\Q(\zeta_{10})\)	None					88.2.i.a	$2$	$0$	\(0\)	\(3\)	\(3\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{3}+(1+\zeta_{10}^{2}+\cdots)q^{5}+\cdots\)
968.2.i.l	$968$	$2$	968.i	11.c	$5$	$4$	$1$	$7.730$	\(\Q(\zeta_{10})\)	None		✓			968.2.a.f	$2$	$0$	\(0\)	\(6\)	\(5\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(2\zeta_{10}-2\zeta_{10}^{2}+2\zeta_{10}^{3})q^{3}+(2+\cdots)q^{5}+\cdots\)
968.2.i.m	$968$	$2$	968.i	11.c	$5$	$4$	$1$	$7.730$	\(\Q(\zeta_{10})\)	None		✓			968.2.a.f	$2$	$0$	\(0\)	\(6\)	\(5\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(2\zeta_{10}-2\zeta_{10}^{2}+2\zeta_{10}^{3})q^{3}+(2+\cdots)q^{5}+\cdots\)
968.2.i.n	$968$	$2$	968.i	11.c	$5$	$8$	$2$	$7.730$	8.0.324000000.3	None		✓			968.2.a.k	$4$	$0$	\(0\)	\(-2\)	\(4\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(\beta _{2}+\beta _{7})q^{3}+(-\beta _{1}-2\beta _{6})q^{5}+(-1+\cdots)q^{7}+\cdots\)
968.2.i.o	$968$	$2$	968.i	11.c	$5$	$8$	$2$	$7.730$	8.0.324000000.3	None		✓			968.2.a.k	$4$	$0$	\(0\)	\(-2\)	\(4\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(\beta _{2}+\beta _{7})q^{3}+(-\beta _{1}-2\beta _{6})q^{5}+(1+\cdots)q^{7}+\cdots\)
968.2.i.p	$968$	$2$	968.i	11.c	$5$	$8$	$2$	$7.730$	8.0.682515625.5	None					88.2.i.b	$2$	$0$	\(0\)	\(-1\)	\(-3\)	\(-7\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(\beta _{1}+\beta _{4}-\beta _{6})q^{3}+(\beta _{3}-\beta _{4}-\beta _{5}+\cdots)q^{5}+\cdots\)
968.2.i.q	$968$	$2$	968.i	11.c	$5$	$8$	$2$	$7.730$	8.0.1305015625.1	None					88.2.a.b	$4$	$0$	\(0\)	\(-1\)	\(-3\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+\beta _{5}q^{3}+(-2-\beta _{1}+2\beta _{2}-2\beta _{3}+\cdots)q^{5}+\cdots\)
968.2.i.r	$968$	$2$	968.i	11.c	$5$	$8$	$2$	$7.730$	8.0.1305015625.1	None					88.2.a.b	$4$	$0$	\(0\)	\(-1\)	\(-3\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+\beta _{5}q^{3}+(-2-\beta _{1}+2\beta _{2}-2\beta _{3}+\cdots)q^{5}+\cdots\)
968.2.i.s	$968$	$2$	968.i	11.c	$5$	$8$	$2$	$7.730$	8.0.682515625.5	None					88.2.i.b	$2$	$0$	\(0\)	\(-1\)	\(2\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-\beta _{2}+\beta _{5})q^{3}+(1-\beta _{2}+\beta _{4}-\beta _{6}+\cdots)q^{5}+\cdots\)
968.2.i.t	$968$	$2$	968.i	11.c	$5$	$8$	$2$	$7.730$	8.0.682515625.5	None					88.2.i.b	$2$	$0$	\(0\)	\(-1\)	\(2\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-\beta _{2}+\beta _{5})q^{3}+(1-\beta _{2}+\beta _{4}-\beta _{6}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(968, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(968, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(88, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(121, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(242, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(484, [\chi])\)\(^{\oplus 2}\)