Space of modular forms of level 289, weight 2, and trivial character

• Label: 289.2.a
• Level: $289$
• Weight: $2$
• Character orbit: 289.a
• Rep. character: $\chi_{289}(1,\cdot)$
• Character field: $\Q$
• Dimension: $15$
• Newform subspaces: $6$
• Sturm bound: $51$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	289.a (trivial)
Character field:			\(\Q\)
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 \(M_{2}(\Gamma_0(289))\).

	Total	New	Old
Modular forms	34	30	4
Cusp forms	17	15	2
Eisenstein series	17	15	2

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(17\)		Total				Cusp				Eisenstein
		All	New	Old		All	New	Old		All	New	Old
\(+\)		\(15\)	\(13\)	\(2\)		\(7\)	\(6\)	\(1\)		\(8\)	\(7\)	\(1\)
\(-\)		\(19\)	\(17\)	\(2\)		\(10\)	\(9\)	\(1\)		\(9\)	\(8\)	\(1\)

Trace form

15 * q + q^2 + 9 * q^4 + 2 * q^5 - 4 * q^7 - 3 * q^8 + 3 * q^9 - 2 * q^10 + 4 * q^13 + 4 * q^14 + 2 * q^15 - 7 * q^16 - 15 * q^18 + 6 * q^19 - 2 * q^20 + 4 * q^21 - 4 * q^23 - 13 * q^25 + 2 * q^26 + 4 * q^28 - 6 * q^29 + 10 * q^30 - 4 * q^31 + 15 * q^32 + 6 * q^33 - 4 * q^35 - 17 * q^36 + 2 * q^37 - 32 * q^38 + 6 * q^40 + 6 * q^41 + 14 * q^42 + 2 * q^43 - 6 * q^45 + 4 * q^46 + 2 * q^47 - 39 * q^49 + 13 * q^50 - 10 * q^52 + 10 * q^55 - 12 * q^56 + 6 * q^58 + 18 * q^59 - 30 * q^60 + 10 * q^61 + 4 * q^62 + 12 * q^63 - 35 * q^64 - 4 * q^65 + 16 * q^66 + 6 * q^67 - 2 * q^69 + 8 * q^70 + 4 * q^71 - q^72 + 6 * q^73 - 2 * q^74 + 16 * q^76 + 14 * q^77 - 12 * q^79 - 2 * q^80 - 49 * q^81 - 6 * q^82 + 12 * q^83 - 40 * q^84 + 2 * q^86 + 12 * q^87 - 4 * q^89 + 6 * q^90 + 8 * q^91 + 4 * q^92 + 16 * q^93 + 16 * q^94 - 8 * q^95 - 2 * q^97 + 31 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(289))\) 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					A-L signs	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		17
289.2.a.a	$289$	$2$	289.a	1.a	$1$	$1$	$1$	$2.308$	\(\Q\)	None	✓				17.2.a.a	$1$	$1$	\(-1\)	\(0\)	\(2\)	\(-4\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+2q^{5}-4q^{7}+3q^{8}-3q^{9}+\cdots\)
289.2.a.b	$289$	$2$	289.a	1.a	$1$	$2$	$2$	$2.308$	\(\Q(\sqrt{13}) \)	None	✓	✓			289.2.a.b	$1$	$1$	\(-1\)	\(-1\)	\(-1\)	\(-3\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(-1+\beta )q^{3}+(1+\beta )q^{4}-\beta q^{5}+\cdots\)
289.2.a.c	$289$	$2$	289.a	1.a	$1$	$2$	$2$	$2.308$	\(\Q(\sqrt{13}) \)	None	✓	✓			289.2.a.b	$1$	$0$	\(-1\)	\(1\)	\(1\)	\(3\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(1-\beta )q^{3}+(1+\beta )q^{4}+\beta q^{5}+\cdots\)
289.2.a.d	$289$	$2$	289.a	1.a	$1$	$3$	$3$	$2.308$	\(\Q(\zeta_{18})^+\)	None	✓	✓	✓		289.2.a.d	$1$	$1$	\(0\)	\(-3\)	\(-6\)	\(0\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(-1-\beta _{2})q^{3}+\beta _{2}q^{4}+(-2+\cdots)q^{5}+\cdots\)
289.2.a.e	$289$	$2$	289.a	1.a	$1$	$3$	$3$	$2.308$	\(\Q(\zeta_{18})^+\)	None	✓	✓			289.2.a.d	$1$	$0$	\(0\)	\(3\)	\(6\)	\(0\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{3}+\beta _{2}q^{4}+(2-\beta _{1}+\cdots)q^{5}+\cdots\)
289.2.a.f	$289$	$2$	289.a	1.a	$1$	$4$	$4$	$2.308$	\(\Q(\zeta_{16})^+\)	None	✓		✓		17.2.d.a	$2$	$0$	\(4\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{2}+(-\beta _{1}+\beta _{3})q^{3}+(1+2\beta _{2}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(289))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(289)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 2}\)