Space of modular forms of level 269, weight 2, and trivial character

• Label: 269.2.a
• Level: $269$
• Weight: $2$
• Character orbit: 269.a
• Rep. character: $\chi_{269}(1,\cdot)$
• Character field: $\Q$
• Dimension: $22$
• Newform subspaces: $3$
• Sturm bound: $45$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 269 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	269.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(45\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(269))\).

	Total	New	Old
Modular forms	23	23	0
Cusp forms	22	22	0
Eisenstein series	1	1	0

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

\(269\)		Total				Cusp				Eisenstein
		All	New	Old		All	New	Old		All	New	Old
\(+\)		\(6\)	\(6\)	\(0\)		\(6\)	\(6\)	\(0\)		\(0\)	\(0\)	\(0\)
\(-\)		\(17\)	\(17\)	\(0\)		\(16\)	\(16\)	\(0\)		\(1\)	\(1\)	\(0\)

Trace form

22 * q + 24 * q^4 - 4 * q^5 - 6 * q^6 + 2 * q^7 + 22 * q^9 + 2 * q^10 + 4 * q^11 - 8 * q^12 - 4 * q^13 - 12 * q^14 - 10 * q^15 + 32 * q^16 - 2 * q^18 + 12 * q^19 - 14 * q^20 + 4 * q^21 - 8 * q^22 + 2 * q^23 - 12 * q^24 + 2 * q^25 - 4 * q^26 + 6 * q^27 + 8 * q^28 - 2 * q^29 + 6 * q^30 + 6 * q^31 - 30 * q^32 + 12 * q^33 - 4 * q^34 + 14 * q^35 + 14 * q^36 + 2 * q^37 - 22 * q^38 - 2 * q^39 + 12 * q^40 + 6 * q^41 - 22 * q^42 + 26 * q^43 + 20 * q^44 - 32 * q^45 + 24 * q^46 + 6 * q^47 - 12 * q^48 + 34 * q^49 - 58 * q^50 + 28 * q^51 - 26 * q^52 - 28 * q^53 - 34 * q^54 - 8 * q^55 - 64 * q^56 - 12 * q^58 - 8 * q^59 - 82 * q^60 - 2 * q^61 - 28 * q^62 - 8 * q^63 + 26 * q^64 - 14 * q^65 - 80 * q^66 + 18 * q^67 - 20 * q^68 + 10 * q^69 - 40 * q^70 - 10 * q^71 - 18 * q^72 + 10 * q^73 + 8 * q^74 + 44 * q^75 + 48 * q^76 - 30 * q^78 + 10 * q^79 - 8 * q^80 - 10 * q^81 - 10 * q^82 - 12 * q^83 + 4 * q^84 - 6 * q^85 + 8 * q^86 - 14 * q^87 - 20 * q^88 - 40 * q^89 - 4 * q^90 + 22 * q^91 + 46 * q^92 - 12 * q^93 + 2 * q^94 + 44 * q^95 - 22 * q^96 - 14 * q^97 + 68 * q^98 + 72 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(269))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		269
269.2.a.a	$269$	$2$	269.a	1.a	$1$	$1$	$1$	$2.148$	\(\Q\)	None	✓	✓			269.2.a.a	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-4\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}+q^{5}-4q^{7}-3q^{9}-3q^{11}+\cdots\)
269.2.a.b	$269$	$2$	269.a	1.a	$1$	$5$	$5$	$2.148$	5.5.65657.1	None	✓	✓	✓		269.2.a.b	$1$	$1$	\(-1\)	\(-5\)	\(-4\)	\(-5\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}+(-1+\beta _{2}+\beta _{3})q^{3}+\beta _{1}q^{4}+\cdots\)
269.2.a.c	$269$	$2$	269.a	1.a	$1$	$16$	$16$	$2.148$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	✓	✓	✓	269.2.a.c	$1$	$0$	\(1\)	\(5\)	\(-1\)	\(11\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{7}q^{3}+(2+\beta _{2})q^{4}+\beta _{12}q^{5}+\cdots\)