Space of modular forms of level 290, weight 2, and trivial character

• Label: 290.2.a
• Level: $290$
• Weight: $2$
• Character orbit: 290.a
• Rep. character: $\chi_{290}(1,\cdot)$
• Character field: $\Q$
• Dimension: $11$
• Newform subspaces: $5$
• Sturm bound: $90$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 290 = 2 \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	290.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(90\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(290))\).

	Total	New	Old
Modular forms	48	11	37
Cusp forms	41	11	30
Eisenstein series	7	0	7

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

\(2\)	\(5\)	\(29\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(3\)	\(1\)	\(2\)		\(3\)	\(1\)	\(2\)		\(0\)	\(0\)	\(0\)
\(+\)	\(+\)	\(-\)	\(-\)		\(8\)	\(2\)	\(6\)		\(7\)	\(2\)	\(5\)		\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(+\)	\(-\)		\(7\)	\(2\)	\(5\)		\(6\)	\(2\)	\(4\)		\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(-\)	\(+\)		\(5\)	\(0\)	\(5\)		\(4\)	\(0\)	\(4\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(+\)	\(-\)		\(6\)	\(3\)	\(3\)		\(5\)	\(3\)	\(2\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)	\(+\)		\(6\)	\(0\)	\(6\)		\(5\)	\(0\)	\(5\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)	\(+\)		\(5\)	\(0\)	\(5\)		\(4\)	\(0\)	\(4\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(-\)	\(-\)		\(8\)	\(3\)	\(5\)		\(7\)	\(3\)	\(4\)		\(1\)	\(0\)	\(1\)
Plus space			\(+\)		\(19\)	\(1\)	\(18\)		\(16\)	\(1\)	\(15\)		\(3\)	\(0\)	\(3\)
Minus space			\(-\)		\(29\)	\(10\)	\(19\)		\(25\)	\(10\)	\(15\)		\(4\)	\(0\)	\(4\)

Trace form

11 * q + q^2 + 4 * q^3 + 11 * q^4 - q^5 + 8 * q^7 + q^8 + 11 * q^9 + q^10 + 4 * q^11 + 4 * q^12 + 10 * q^13 - 4 * q^14 - 4 * q^15 + 11 * q^16 + 2 * q^17 + 13 * q^18 + 12 * q^19 - q^20 - 8 * q^21 - 16 * q^23 + 11 * q^25 + 6 * q^26 - 8 * q^27 + 8 * q^28 - q^29 - 4 * q^30 - 8 * q^31 + q^32 - 24 * q^33 - 6 * q^34 - 4 * q^35 + 11 * q^36 - 2 * q^37 - 8 * q^38 - 16 * q^39 + q^40 + 6 * q^41 - 16 * q^42 + 12 * q^43 + 4 * q^44 + 3 * q^45 - 12 * q^46 - 32 * q^47 + 4 * q^48 + 7 * q^49 + q^50 - 16 * q^51 + 10 * q^52 + 2 * q^53 - 24 * q^54 + 4 * q^55 - 4 * q^56 - 32 * q^57 + q^58 - 16 * q^59 - 4 * q^60 + 10 * q^61 - 20 * q^62 - 32 * q^63 + 11 * q^64 - 2 * q^65 - 24 * q^66 + 12 * q^67 + 2 * q^68 - 48 * q^69 - 4 * q^70 - 32 * q^71 + 13 * q^72 - 6 * q^73 - 6 * q^74 + 4 * q^75 + 12 * q^76 - 24 * q^77 - 24 * q^78 + 16 * q^79 - q^80 + 19 * q^81 - 14 * q^82 - 36 * q^83 - 8 * q^84 - 14 * q^85 + 16 * q^86 - 4 * q^87 - 26 * q^89 - 3 * q^90 + 16 * q^91 - 16 * q^92 - 8 * q^93 - 16 * q^94 + 4 * q^95 + 42 * q^97 + 9 * q^98 - 12 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(290))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	5	29
290.2.a.a	$290$	$2$	290.a	1.a	$1$	$1$	$1$	$2.316$	\(\Q\)	None	✓	✓	✓	✓	290.2.a.a	$1$	$1$	\(-1\)	\(0\)	\(-1\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{5}-2q^{7}-q^{8}-3q^{9}+\cdots\)
290.2.a.b	$290$	$2$	290.a	1.a	$1$	$2$	$2$	$2.316$	\(\Q(\sqrt{13}) \)	None	✓	✓	✓	✓	290.2.a.b	$1$	$0$	\(-2\)	\(1\)	\(-2\)	\(5\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(1-\beta )q^{3}+q^{4}-q^{5}+(-1+\cdots)q^{6}+\cdots\)
290.2.a.c	$290$	$2$	290.a	1.a	$1$	$2$	$2$	$2.316$	\(\Q(\sqrt{13}) \)	None	✓	✓	✓	✓	290.2.a.c	$1$	$0$	\(-2\)	\(1\)	\(2\)	\(3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(1-\beta )q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots\)
290.2.a.d	$290$	$2$	290.a	1.a	$1$	$3$	$3$	$2.316$	3.3.469.1	None	✓	✓	✓	✓	290.2.a.d	$1$	$0$	\(3\)	\(-1\)	\(3\)	\(-1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta _{2}q^{3}+q^{4}+q^{5}+\beta _{2}q^{6}+\cdots\)
290.2.a.e	$290$	$2$	290.a	1.a	$1$	$3$	$3$	$2.316$	3.3.621.1	None	✓	✓	✓	✓	290.2.a.e	$1$	$0$	\(3\)	\(3\)	\(-3\)	\(3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(1-\beta _{1})q^{3}+q^{4}-q^{5}+(1-\beta _{1}+\cdots)q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(290))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(290)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(58))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(145))\)\(^{\oplus 2}\)