Space of modular forms of level 28 and weight 5

• Label: 28.5
• Level: 28
• Weight: 5
• Dimension: 48
• Nonzero newspaces: 4
• Newform subspaces: 4
• Sturm bound: 240
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 28 = 2^{2} \cdot 7 \)
Weight:	\( k \)	=	\( 5 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 4 \)
Sturm bound:			\(240\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(28))\).

	Total	New	Old
Modular forms	111	56	55
Cusp forms	81	48	33
Eisenstein series	30	8	22

Trace form

48 * q + 5 * q^2 + 9 * q^3 - 35 * q^4 - 5 * q^5 - 6 * q^6 + 52 * q^7 - 13 * q^8 - 12 * q^9 + 182 * q^10 + 171 * q^11 + 342 * q^12 + 464 * q^13 - 327 * q^14 - 774 * q^15 - 1343 * q^16 - 1757 * q^17 + 63 * q^18 - 747 * q^19 + 1576 * q^20 + 1923 * q^21 - 432 * q^22 + 1719 * q^23 - 1866 * q^24 + 4220 * q^25 - 2720 * q^26 + 1317 * q^28 - 5000 * q^29 + 1842 * q^30 - 5355 * q^31 + 2675 * q^32 - 4029 * q^33 + 7358 * q^34 + 4005 * q^35 + 3237 * q^36 + 5917 * q^37 + 1572 * q^38 + 8412 * q^39 - 1300 * q^40 + 6064 * q^41 + 1146 * q^42 - 5968 * q^43 - 3468 * q^44 - 10470 * q^45 - 11538 * q^46 - 9747 * q^47 - 19746 * q^48 - 5448 * q^49 - 16443 * q^50 + 4869 * q^51 + 2516 * q^52 - 1667 * q^53 + 3558 * q^54 + 639 * q^56 - 2874 * q^57 + 6026 * q^58 - 2943 * q^59 + 31488 * q^60 + 24143 * q^61 + 28344 * q^62 + 14676 * q^63 + 19225 * q^64 + 6320 * q^65 + 21042 * q^66 + 6559 * q^67 + 7738 * q^68 - 19500 * q^69 - 12510 * q^70 - 4032 * q^71 - 28497 * q^72 + 4967 * q^73 - 28328 * q^74 - 3438 * q^75 - 51918 * q^76 + 6069 * q^77 - 59592 * q^78 - 15737 * q^79 - 49976 * q^80 - 6759 * q^81 - 41998 * q^82 + 29106 * q^84 + 17614 * q^85 + 62100 * q^86 + 40014 * q^87 + 67680 * q^88 - 16625 * q^89 + 103236 * q^90 - 8184 * q^91 + 84792 * q^92 - 5517 * q^93 + 71934 * q^94 - 24399 * q^95 + 37146 * q^96 + 5840 * q^97 - 10711 * q^98 + 9288 * q^99

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(28))\)

We only show spaces with odd 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
28.5.b	\(\chi_{28}(13, \cdot)\)	28.5.b.a	2	1
28.5.c	\(\chi_{28}(15, \cdot)\)	28.5.c.a	12	1
28.5.g	\(\chi_{28}(11, \cdot)\)	28.5.g.a	28	2
28.5.h	\(\chi_{28}(5, \cdot)\)	28.5.h.a	6	2

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(28))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(28)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 2}\)