Space of modular forms of level 949, weight 2, and trivial character

• Label: 949.2.a
• Level: $949$
• Weight: $2$
• Character orbit: 949.a
• Rep. character: $\chi_{949}(1,\cdot)$
• Character field: $\Q$
• Dimension: $73$
• Newform subspaces: $6$
• Sturm bound: $172$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 949 = 13 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	949.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(172\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(949))\).

	Total	New	Old
Modular forms	86	73	13
Cusp forms	83	73	10
Eisenstein series	3	0	3

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

\(13\)	\(73\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(20\)	\(18\)	\(2\)		\(20\)	\(18\)	\(2\)		\(0\)	\(0\)	\(0\)
\(+\)	\(-\)	\(-\)		\(23\)	\(19\)	\(4\)		\(22\)	\(19\)	\(3\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)		\(23\)	\(20\)	\(3\)		\(22\)	\(20\)	\(2\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)		\(20\)	\(16\)	\(4\)		\(19\)	\(16\)	\(3\)		\(1\)	\(0\)	\(1\)
Plus space		\(+\)		\(40\)	\(34\)	\(6\)		\(39\)	\(34\)	\(5\)		\(1\)	\(0\)	\(1\)
Minus space		\(-\)		\(46\)	\(39\)	\(7\)		\(44\)	\(39\)	\(5\)		\(2\)	\(0\)	\(2\)

Trace form

73 * q - q^2 + 67 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^7 - 9 * q^8 + 73 * q^9 - 10 * q^10 - 4 * q^11 - 16 * q^12 - q^13 - 24 * q^14 - 16 * q^15 + 43 * q^16 + 2 * q^17 - q^18 + 4 * q^19 + 2 * q^20 - 32 * q^21 - 16 * q^22 - 8 * q^24 + 75 * q^25 - 3 * q^26 - 24 * q^27 + 16 * q^28 - 22 * q^29 + 28 * q^30 - 16 * q^31 - 9 * q^32 + 24 * q^33 - 10 * q^34 - 24 * q^35 + 71 * q^36 - 22 * q^37 - 4 * q^39 - 34 * q^40 + 10 * q^41 + 4 * q^42 - 56 * q^44 - 26 * q^45 - 56 * q^46 - 16 * q^47 - 16 * q^48 + 77 * q^49 + 9 * q^50 - 8 * q^51 - 7 * q^52 - 18 * q^53 - 8 * q^54 + 36 * q^55 - 16 * q^56 + 44 * q^57 + 18 * q^58 - 20 * q^60 - 18 * q^61 - 44 * q^62 - 16 * q^63 - 5 * q^64 + 6 * q^65 + 76 * q^66 - 24 * q^67 - 38 * q^68 - 44 * q^69 - 16 * q^70 + 20 * q^71 - 69 * q^72 - 3 * q^73 + 10 * q^74 - 16 * q^75 + 8 * q^76 + 16 * q^77 + 8 * q^78 + 4 * q^79 - 50 * q^80 + 49 * q^81 + 14 * q^82 - 48 * q^83 - 40 * q^84 - 16 * q^85 + 44 * q^86 - 20 * q^87 - 72 * q^88 - 18 * q^89 - 2 * q^90 + 8 * q^91 + 40 * q^92 - 32 * q^94 - 32 * q^95 + 60 * q^96 + 18 * q^97 + 15 * q^98 - 8 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(949))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		13	73
949.2.a.a	$949$	$2$	949.a	1.a	$1$	$2$	$2$	$7.578$	\(\Q(\sqrt{5}) \)	None	✓	✓			949.2.a.a	$1$	$0$	\(-1\)	\(3\)	\(4\)	\(2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(1+\beta )q^{3}+(-1+\beta )q^{4}+(1+\cdots)q^{5}+\cdots\)
949.2.a.b	$949$	$2$	949.a	1.a	$1$	$2$	$2$	$7.578$	\(\Q(\sqrt{5}) \)	None	✓	✓			949.2.a.b	$1$	$0$	\(3\)	\(3\)	\(0\)	\(6\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+(2-\beta )q^{3}+3\beta q^{4}+(1+\cdots)q^{5}+\cdots\)
949.2.a.c	$949$	$2$	949.a	1.a	$1$	$16$	$16$	$7.578$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	✓	✓	✓	949.2.a.c	$1$	$1$	\(-3\)	\(-11\)	\(-6\)	\(1\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(-1+\beta _{10})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots\)
949.2.a.d	$949$	$2$	949.a	1.a	$1$	$16$	$16$	$7.578$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	✓	✓		949.2.a.d	$1$	$0$	\(-1\)	\(3\)	\(4\)	\(-3\)		$-$	$+$	$-$	$5$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{11}q^{3}+(1+\beta _{2})q^{4}-\beta _{12}q^{5}+\cdots\)
949.2.a.e	$949$	$2$	949.a	1.a	$1$	$18$	$18$	$7.578$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	✓	✓	✓	949.2.a.e	$1$	$1$	\(-3\)	\(-3\)	\(-12\)	\(-7\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{8}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
949.2.a.f	$949$	$2$	949.a	1.a	$1$	$19$	$19$	$7.578$	\(\mathbb{Q}[x]/(x^{19} - \cdots)\)	None	✓	✓	✓	✓	949.2.a.f	$1$	$0$	\(4\)	\(5\)	\(8\)	\(5\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{8}q^{3}+(1+\beta _{2})q^{4}-\beta _{10}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(949))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(949)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(73))\)\(^{\oplus 2}\)