Space of modular forms of level 29 and weight 6

• Label: 29.6
• Level: 29
• Weight: 6
• Dimension: 161
• Nonzero newspaces: 4
• Newform subspaces: 5
• Sturm bound: 420
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 29 \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 5 \)
Sturm bound:			\(420\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(29))\).

	Total	New	Old
Modular forms	189	187	2
Cusp forms	161	161	0
Eisenstein series	28	26	2

Trace form

161 * q - 14 * q^2 - 14 * q^3 - 14 * q^4 - 14 * q^5 - 14 * q^6 - 14 * q^7 - 14 * q^8 - 14 * q^9 - 14 * q^10 - 14 * q^11 - 14 * q^12 - 14 * q^13 - 14 * q^14 - 14 * q^15 - 14 * q^16 - 14 * q^17 - 14 * q^18 - 14 * q^19 - 13790 * q^20 + 6846 * q^21 + 16674 * q^22 + 7980 * q^23 + 26866 * q^24 - 882 * q^25 - 13314 * q^26 - 27272 * q^27 - 43932 * q^28 - 21154 * q^29 - 46732 * q^30 - 5754 * q^31 + 14322 * q^32 + 31948 * q^33 + 42686 * q^34 + 42518 * q^35 + 127666 * q^36 + 14840 * q^37 - 1246 * q^38 - 56154 * q^39 - 106190 * q^40 - 14 * q^41 - 14 * q^42 - 14 * q^43 - 114660 * q^44 - 116249 * q^45 - 4144 * q^46 + 52934 * q^47 + 313474 * q^48 + 163002 * q^49 + 239988 * q^50 + 90202 * q^51 + 63938 * q^52 - 32837 * q^53 - 193928 * q^54 - 266686 * q^55 - 291424 * q^56 - 181972 * q^57 - 536102 * q^58 - 78120 * q^59 - 346710 * q^60 - 58758 * q^61 + 17724 * q^62 + 172354 * q^63 + 366772 * q^64 + 262003 * q^65 + 573538 * q^66 + 314202 * q^67 + 531048 * q^68 + 241402 * q^69 - 239694 * q^70 - 372988 * q^71 - 610820 * q^72 - 430661 * q^73 + 135744 * q^74 + 487116 * q^75 + 786674 * q^76 + 435456 * q^77 + 537138 * q^78 + 83174 * q^79 + 185010 * q^80 - 124446 * q^81 - 170478 * q^82 - 264838 * q^83 - 1022168 * q^84 - 585578 * q^85 - 1035468 * q^86 - 511644 * q^87 - 1126300 * q^88 - 391944 * q^89 - 568456 * q^90 - 174818 * q^91 + 29554 * q^92 + 146762 * q^93 + 286482 * q^94 + 839874 * q^95 + 384552 * q^96 - 672455 * q^97 + 772408 * q^98 + 905996 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(29))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label	\(\chi\)	Newforms	Dimension	\(\chi\) degree
29.6.a	\(\chi_{29}(1, \cdot)\)	29.6.a.a	4	1
		29.6.a.b	7
29.6.b	\(\chi_{29}(28, \cdot)\)	29.6.b.a	12	1
29.6.d	\(\chi_{29}(7, \cdot)\)	29.6.d.a	66	6
29.6.e	\(\chi_{29}(4, \cdot)\)	29.6.e.a	72	6