Space of modular forms of level 29, weight 4, and trivial character

• Label: 29.4.a
• Level: $29$
• Weight: $4$
• Character orbit: 29.a
• Rep. character: $\chi_{29}(1,\cdot)$
• Character field: $\Q$
• Dimension: $7$
• Newform subspaces: $2$
• Sturm bound: $10$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	29.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(10\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(29))\).

	Total	New	Old
Modular forms	9	7	2
Cusp forms	7	7	0
Eisenstein series	2	0	2

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

\(29\)		Total				Cusp				Eisenstein
		All	New	Old		All	New	Old		All	New	Old
\(+\)		\(6\)	\(5\)	\(1\)		\(5\)	\(5\)	\(0\)		\(1\)	\(0\)	\(1\)
\(-\)		\(3\)	\(2\)	\(1\)		\(2\)	\(2\)	\(0\)		\(1\)	\(0\)	\(1\)

Trace form

7 * q - 2 * q^2 - 2 * q^3 + 16 * q^4 + 32 * q^6 + 24 * q^7 - 66 * q^8 + 65 * q^9 - 38 * q^10 - 14 * q^11 - 150 * q^12 - 12 * q^13 - 136 * q^14 - 72 * q^15 + 164 * q^16 + 126 * q^17 - 20 * q^18 - 6 * q^19 + 24 * q^20 - 40 * q^21 - 220 * q^22 + 216 * q^23 + 356 * q^24 + 71 * q^25 - 22 * q^26 + 112 * q^27 + 540 * q^28 - 87 * q^29 - 256 * q^30 + 126 * q^31 - 670 * q^32 - 2 * q^33 + 216 * q^34 + 188 * q^35 - 660 * q^36 + 690 * q^37 - 148 * q^38 + 68 * q^39 - 346 * q^40 - 1118 * q^41 + 284 * q^42 - 526 * q^43 + 1210 * q^44 - 1186 * q^45 + 720 * q^46 + 118 * q^47 - 2402 * q^48 - 441 * q^49 + 884 * q^50 - 288 * q^51 + 1820 * q^52 + 448 * q^53 + 700 * q^54 + 84 * q^55 - 1192 * q^56 + 760 * q^57 - 58 * q^58 - 460 * q^59 + 666 * q^60 - 330 * q^61 + 1292 * q^62 + 1748 * q^63 + 2712 * q^64 - 1942 * q^65 + 3262 * q^66 + 1484 * q^67 - 88 * q^68 - 2804 * q^69 - 2752 * q^70 - 1352 * q^71 - 3680 * q^72 - 1302 * q^73 - 2368 * q^74 + 4234 * q^75 + 2220 * q^76 - 2888 * q^77 - 1068 * q^78 + 530 * q^79 - 404 * q^80 + 3591 * q^81 + 604 * q^82 + 1724 * q^83 - 2800 * q^84 - 1640 * q^85 + 3452 * q^86 - 522 * q^87 - 5560 * q^88 + 1626 * q^89 - 2864 * q^90 + 1748 * q^91 + 2824 * q^92 + 2186 * q^93 - 6640 * q^94 + 3856 * q^95 + 6744 * q^96 + 1586 * q^97 - 3890 * q^98 - 5094 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(29))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		29
29.4.a.a	$29$	$4$	29.a	1.a	$1$	$2$	$2$	$1.711$	\(\Q(\sqrt{2}) \)	None	✓	✓	✓	✓	29.4.a.a	$1$	$1$	\(-2\)	\(-10\)	\(-10\)	\(-16\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+(-5-3\beta )q^{3}+(-5+\cdots)q^{4}+\cdots\)
29.4.a.b	$29$	$4$	29.a	1.a	$1$	$5$	$5$	$1.711$	5.5.13458092.1	None	✓	✓	✓	✓	29.4.a.b	$1$	$0$	\(0\)	\(8\)	\(10\)	\(40\)		$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1-\beta _{1}-\beta _{3}-\beta _{4})q^{3}+(6+\cdots)q^{4}+\cdots\)