Space of modular forms of level 28 and weight 8

• Label: 28.8
• Level: 28
• Weight: 8
• Dimension: 92
• Nonzero newspaces: 4
• Newform subspaces: 6
• Sturm bound: 384
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 28 = 2^{2} \cdot 7 \)
Weight:	\( k \)	=	\( 8 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 6 \)
Sturm bound:			\(384\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(28))\).

	Total	New	Old
Modular forms	183	104	79
Cusp forms	153	92	61
Eisenstein series	30	12	18

Trace form

92 * q - 3 * q^2 + 27 * q^3 - 3 * q^4 - 9 * q^5 + 332 * q^7 - 867 * q^8 - 5184 * q^9 + 9708 * q^10 + 10335 * q^11 - 13848 * q^12 - 31328 * q^13 - 19647 * q^14 + 15918 * q^15 + 47721 * q^16 - 9837 * q^17 + 25581 * q^18 + 11005 * q^19 - 34659 * q^21 - 29490 * q^22 + 9321 * q^23 - 142644 * q^24 - 153802 * q^25 + 205116 * q^26 + 55710 * q^27 + 417285 * q^28 - 102240 * q^29 - 9540 * q^30 - 35861 * q^31 - 1348203 * q^32 + 643869 * q^33 + 906963 * q^35 + 2521149 * q^36 - 765485 * q^37 + 404100 * q^38 - 533346 * q^39 - 1872348 * q^40 - 2262948 * q^41 - 2942340 * q^42 - 1208984 * q^43 + 1624158 * q^44 + 3246186 * q^45 + 3456402 * q^46 + 1869093 * q^47 + 631412 * q^49 - 2861151 * q^50 - 195471 * q^51 - 3374784 * q^52 - 3128601 * q^53 + 5449860 * q^54 - 1136538 * q^55 + 3777489 * q^56 - 4732614 * q^57 - 4692078 * q^58 + 1161459 * q^59 - 3444432 * q^60 + 5289295 * q^61 + 12004710 * q^63 + 2674617 * q^64 + 4600014 * q^65 + 1899192 * q^66 - 5537021 * q^67 - 3418884 * q^68 - 24142770 * q^69 - 399624 * q^70 - 13279392 * q^71 - 8177415 * q^72 + 6871315 * q^73 - 8501106 * q^74 + 38150052 * q^75 + 36769593 * q^77 + 9240072 * q^78 + 2832073 * q^79 + 24461112 * q^80 - 44763117 * q^81 - 12674916 * q^82 - 41841048 * q^83 - 12815124 * q^84 - 39615042 * q^85 + 23964678 * q^86 + 25583382 * q^87 + 22325874 * q^88 + 69189915 * q^89 + 43871512 * q^91 - 39725286 * q^92 + 11401641 * q^93 - 16365540 * q^94 - 50914329 * q^95 + 15981144 * q^96 - 43794260 * q^97 + 16573521 * q^98 - 95711028 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(28))\)

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
28.8.a	\(\chi_{28}(1, \cdot)\)	28.8.a.a	2	1
		28.8.a.b	2
28.8.d	\(\chi_{28}(27, \cdot)\)	28.8.d.a	2	1
		28.8.d.b	24
28.8.e	\(\chi_{28}(9, \cdot)\)	28.8.e.a	10	2
28.8.f	\(\chi_{28}(3, \cdot)\)	28.8.f.a	52	2

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(28))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(28)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 1}\)