Space of modular forms of level 28 and weight 2

• Label: 28.2
• Level: 28
• Weight: 2
• Dimension: 8
• Nonzero newspaces: 3
• Newform subspaces: 3
• Sturm bound: 96
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 28 = 2^{2} \cdot 7 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 3 \)
Newform subspaces:			\( 3 \)
Sturm bound:			\(96\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(28))\).

	Total	New	Old
Modular forms	39	20	19
Cusp forms	10	8	2
Eisenstein series	29	12	17

Trace form

8 * q - 3 * q^2 - q^3 - 3 * q^4 - 9 * q^5 - 4 * q^7 - 3 * q^8 - 4 * q^9 + 6 * q^10 + 3 * q^11 + 12 * q^12 + 4 * q^13 + 9 * q^14 + 6 * q^15 + 9 * q^16 - 9 * q^17 + 3 * q^18 + q^19 + 5 * q^21 - 18 * q^22 - 3 * q^23 - 12 * q^24 + 2 * q^25 - 12 * q^26 - 10 * q^27 - 27 * q^28 - 6 * q^30 + 7 * q^31 - 3 * q^32 + 9 * q^33 + 15 * q^35 + 9 * q^36 + 7 * q^37 + 18 * q^38 - 2 * q^39 + 12 * q^40 + 12 * q^41 + 12 * q^42 - 8 * q^43 + 18 * q^44 + 6 * q^45 + 12 * q^46 + 9 * q^47 - 16 * q^49 + 3 * q^50 - 3 * q^51 - 21 * q^53 - 18 * q^54 - 18 * q^55 + 9 * q^56 - 38 * q^57 - 6 * q^58 - 9 * q^59 - 12 * q^60 - 17 * q^61 - 10 * q^63 + 9 * q^64 + 6 * q^65 - 6 * q^66 + 7 * q^67 + 6 * q^69 + 6 * q^70 - 15 * q^72 + 31 * q^73 - 12 * q^74 - 4 * q^75 + 21 * q^77 + 24 * q^78 + 13 * q^79 - 24 * q^80 + 35 * q^81 + 12 * q^82 + 24 * q^83 + 30 * q^85 - 18 * q^86 + 6 * q^87 + 18 * q^88 + 39 * q^89 - 8 * q^91 - 6 * q^92 + 13 * q^93 - 30 * q^94 + 3 * q^95 - 24 * q^96 - 20 * q^97 - 15 * q^98 + 12 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)

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
28.2.a	\(\chi_{28}(1, \cdot)\)	None	0	1
28.2.d	\(\chi_{28}(27, \cdot)\)	28.2.d.a	2	1
28.2.e	\(\chi_{28}(9, \cdot)\)	28.2.e.a	2	2
28.2.f	\(\chi_{28}(3, \cdot)\)	28.2.f.a	4	2

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(28))\) into lower level spaces

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