Space of modular forms of level 289, weight 2, and Character 289.d

• Label: 289.2.d
• Level: $289$
• Weight: $2$
• Character orbit: 289.d
• Rep. character: $\chi_{289}(110,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $60$
• Newform subspaces: $6$
• Sturm bound: $51$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	289.d (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q(\zeta_{8})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(51\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(289, [\chi])\).

	Total	New	Old
Modular forms	140	116	24
Cusp forms	68	60	8
Eisenstein series	72	56	16

Trace form

60 * q + 4 * q^2 + 4 * q^3 - 4 * q^6 + 4 * q^7 - 4 * q^8 - 8 * q^9 - 4 * q^10 + 4 * q^11 + 4 * q^12 - 4 * q^14 + 8 * q^15 + 44 * q^16 - 36 * q^18 - 8 * q^19 - 4 * q^20 - 12 * q^22 - 4 * q^23 - 12 * q^24 + 4 * q^25 + 4 * q^26 - 8 * q^27 - 4 * q^28 + 4 * q^29 + 12 * q^31 - 4 * q^32 - 24 * q^33 - 56 * q^35 + 8 * q^40 + 4 * q^41 + 8 * q^42 + 8 * q^43 + 20 * q^44 - 12 * q^45 - 20 * q^46 - 12 * q^48 - 8 * q^49 - 76 * q^50 - 48 * q^52 + 4 * q^53 + 8 * q^54 + 20 * q^56 + 24 * q^57 + 8 * q^60 + 12 * q^62 + 12 * q^63 + 4 * q^65 - 8 * q^66 - 56 * q^67 + 24 * q^69 + 8 * q^70 - 20 * q^71 + 28 * q^73 - 20 * q^74 + 12 * q^75 - 8 * q^76 - 8 * q^77 + 8 * q^78 + 4 * q^79 - 4 * q^82 - 16 * q^83 + 128 * q^84 - 16 * q^86 - 16 * q^87 - 12 * q^88 - 4 * q^90 + 28 * q^92 - 24 * q^93 + 24 * q^94 + 8 * q^95 + 20 * q^96 - 24 * q^97 + 4 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(289, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
289.2.d.a	$289$	$2$	289.d	17.d	$8$	$4$	$1$	$2.308$	\(\Q(\zeta_{8})\)	None					17.2.d.a	$2$	$0$	\(-4\)	\(4\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{8}]$	\(q+(-1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(1+\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{3}+\cdots\)
289.2.d.b	$289$	$2$	289.d	17.d	$8$	$4$	$1$	$2.308$	\(\Q(\zeta_{8})\)	None					17.2.d.a	$2$	$0$	\(4\)	\(-4\)	\(-4\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{8}]$	\(q+(1-\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(-1-\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{3}+\cdots\)
289.2.d.c	$289$	$2$	289.d	17.d	$8$	$4$	$1$	$2.308$	\(\Q(\zeta_{8})\)	None					17.2.d.a	$2$	$0$	\(4\)	\(4\)	\(4\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{8}]$	\(q+(1-\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(1+\zeta_{8}-\zeta_{8}^{2}+\cdots)q^{3}+\cdots\)
289.2.d.d	$289$	$2$	289.d	17.d	$8$	$8$	$2$	$2.308$	\(\Q(\zeta_{16})\)	None					17.2.a.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{8}]$	\(q+\beta_{2} q^{2}-\beta_{4} q^{4}-\beta_{7} q^{5}-2\beta_1 q^{7}+\cdots\)
289.2.d.e	$289$	$2$	289.d	17.d	$8$	$16$	$4$	$2.308$	16.0.\(\cdots\).1	None		✓			289.2.a.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{8}]$	\(q+(\beta _{3}+\beta _{5})q^{2}+(-\beta _{6}-\beta _{7})q^{3}+(-2\beta _{8}+\cdots)q^{4}+\cdots\)
289.2.d.f	$289$	$2$	289.d	17.d	$8$	$24$	$6$	$2.308$		None		✓	✓		289.2.a.d	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{8}]$

Decomposition of \(S_{2}^{\mathrm{old}}(289, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(289, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 2}\)