Space of modular forms of level 28 and weight 6

• Label: 28.6
• Level: 28
• Weight: 6
• Dimension: 62
• Nonzero newspaces: 4
• Newform subspaces: 7
• Sturm bound: 288
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 28 = 2^{2} \cdot 7 \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 7 \)
Sturm bound:			\(288\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(28))\).

	Total	New	Old
Modular forms	135	74	61
Cusp forms	105	62	43
Eisenstein series	30	12	18

Trace form

62 * q - 3 * q^2 + 15 * q^3 - 3 * q^4 - 147 * q^5 - 28 * q^7 + 261 * q^8 - 54 * q^9 - 804 * q^10 - 813 * q^11 + 1632 * q^12 + 532 * q^13 + 1857 * q^14 + 3678 * q^15 - 1143 * q^16 - 2019 * q^17 - 6747 * q^18 - 4559 * q^19 - 8877 * q^21 + 13206 * q^22 + 6393 * q^23 + 564 * q^24 + 7592 * q^25 - 8892 * q^26 + 12726 * q^27 - 16827 * q^28 + 15516 * q^29 + 5364 * q^30 - 6293 * q^31 + 8397 * q^32 - 36945 * q^33 - 36393 * q^35 - 10011 * q^36 - 11831 * q^37 - 5652 * q^38 + 41478 * q^39 + 35052 * q^40 + 29232 * q^41 + 30756 * q^42 + 63136 * q^43 + 20094 * q^44 + 7554 * q^45 + 16242 * q^46 - 58923 * q^47 - 51034 * q^49 - 79551 * q^50 - 38547 * q^51 - 61776 * q^52 + 11541 * q^53 - 30996 * q^54 + 130662 * q^55 + 27729 * q^56 + 42798 * q^57 - 112734 * q^58 - 45057 * q^59 - 118680 * q^60 - 86219 * q^61 - 178626 * q^63 + 99945 * q^64 + 109026 * q^65 + 221808 * q^66 + 112567 * q^67 + 25020 * q^68 + 136458 * q^69 + 160488 * q^70 + 149184 * q^71 + 259401 * q^72 - 293459 * q^73 + 267870 * q^74 - 228948 * q^75 - 128985 * q^77 - 216552 * q^78 - 16559 * q^79 - 277224 * q^80 + 457635 * q^81 - 391836 * q^82 - 43008 * q^83 - 573972 * q^84 + 95226 * q^85 - 274818 * q^86 - 81234 * q^87 - 198990 * q^88 - 163515 * q^89 - 81032 * q^91 + 288954 * q^92 - 268161 * q^93 + 359988 * q^94 - 63393 * q^95 + 1061736 * q^96 + 409024 * q^97 + 828393 * q^98 + 381828 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(28))\)

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
28.6.a	\(\chi_{28}(1, \cdot)\)	28.6.a.a	1	1
		28.6.a.b	1
28.6.d	\(\chi_{28}(27, \cdot)\)	28.6.d.a	2	1
		28.6.d.b	16
28.6.e	\(\chi_{28}(9, \cdot)\)	28.6.e.a	2	2
		28.6.e.b	4
28.6.f	\(\chi_{28}(3, \cdot)\)	28.6.f.a	36	2

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(28))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(28)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 2}\)