Space of modular forms of level 29, weight 6, and trivial character

• Label: 29.6.a
• Level: $29$
• Weight: $6$
• Character orbit: 29.a
• Rep. character: $\chi_{29}(1,\cdot)$
• Character field: $\Q$
• Dimension: $11$
• Newform subspaces: $2$
• Sturm bound: $15$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	29.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(15\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(29))\).

	Total	New	Old
Modular forms	13	11	2
Cusp forms	11	11	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.

\(29\)	Dim
\(+\)	\(4\)
\(-\)	\(7\)

Trace form

11 * q + 4 * q^2 - 2 * q^3 + 164 * q^4 - 36 * q^5 - 172 * q^6 - 24 * q^7 + 438 * q^8 + 725 * q^9 + 134 * q^10 + 982 * q^11 + 234 * q^12 - 52 * q^13 - 1240 * q^14 + 318 * q^15 - 172 * q^16 - 690 * q^17 - 2390 * q^18 + 1896 * q^19 - 3528 * q^20 - 3208 * q^21 - 576 * q^22 - 5724 * q^23 + 2468 * q^24 + 7351 * q^25 - 15082 * q^26 + 8410 * q^27 - 452 * q^28 + 2523 * q^29 - 8548 * q^30 - 11418 * q^31 + 14450 * q^32 + 23830 * q^33 + 13228 * q^34 - 15856 * q^35 - 8040 * q^36 - 5842 * q^37 + 23276 * q^38 + 24662 * q^39 + 22886 * q^40 + 18706 * q^41 - 53596 * q^42 - 1922 * q^43 - 8006 * q^44 - 490 * q^45 - 19992 * q^46 + 38050 * q^47 + 16654 * q^48 + 48883 * q^49 + 2174 * q^50 + 36636 * q^51 - 63364 * q^52 - 49784 * q^53 + 4216 * q^54 - 78226 * q^55 - 45256 * q^56 - 39596 * q^57 + 3364 * q^58 + 2048 * q^59 - 155622 * q^60 + 152314 * q^61 - 24136 * q^62 - 61144 * q^63 - 30904 * q^64 - 51370 * q^65 - 40034 * q^66 + 95156 * q^67 + 105824 * q^68 - 48452 * q^69 + 271984 * q^70 - 100340 * q^71 + 143656 * q^72 - 92558 * q^73 - 23788 * q^74 - 51092 * q^75 + 219948 * q^76 + 34552 * q^77 + 49368 * q^78 + 105982 * q^79 + 201148 * q^80 - 187977 * q^81 - 32208 * q^82 - 60040 * q^83 - 72160 * q^84 - 85488 * q^85 - 279304 * q^86 + 45414 * q^87 + 97240 * q^88 + 41058 * q^89 + 97636 * q^90 - 74528 * q^91 - 136376 * q^92 - 252814 * q^93 + 469468 * q^94 + 15676 * q^95 - 195624 * q^96 - 167702 * q^97 + 213172 * q^98 + 467388 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(29))\) 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
29.6.a.a	$29$	$6$	29.a	1.a	$1$	$4$	$4$	$4.651$	4.4.3257317.1	None	✓	✓	✓	✓	29.6.a.a	$1$	$1$	\(0\)	\(-28\)	\(-68\)	\(-208\)		$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}+(-7+\beta _{1}+\beta _{2})q^{3}+(2-3\beta _{1}+\cdots)q^{4}+\cdots\)
29.6.a.b	$29$	$6$	29.a	1.a	$1$	$7$	$7$	$4.651$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓	✓	✓	29.6.a.b	$1$	$0$	\(4\)	\(26\)	\(32\)	\(184\)		$-$	$-$	$2^{5}$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(4+\beta _{5})q^{3}+(23-3\beta _{1}+\cdots)q^{4}+\cdots\)