Space of modular forms of level 17 and weight 2

• Label: 17.2
• Level: 17
• Weight: 2
• Dimension: 5
• Nonzero newspaces: 2
• Newform subspaces: 2
• Sturm bound: 48
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 17 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 2 \)
Sturm bound:			\(48\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(17))\).

	Total	New	Old
Modular forms	20	20	0
Cusp forms	5	5	0
Eisenstein series	15	15	0

Trace form

5 * q - 5 * q^2 - 4 * q^3 - q^4 - 2 * q^5 + 4 * q^6 + 7 * q^8 + 5 * q^9 + 6 * q^10 - 4 * q^11 - 4 * q^12 - 2 * q^13 - 8 * q^15 - 13 * q^16 + q^17 - 9 * q^18 + 4 * q^19 + 6 * q^20 + 12 * q^22 + 8 * q^23 + 12 * q^24 - 5 * q^25 - 2 * q^26 + 8 * q^27 + 2 * q^29 - 8 * q^31 - q^32 - 21 * q^34 + 3 * q^36 - 2 * q^37 + 4 * q^38 - 14 * q^40 - 10 * q^41 - 8 * q^42 - 4 * q^43 - 20 * q^44 + 18 * q^45 + 16 * q^46 + 12 * q^48 + 17 * q^49 + 21 * q^50 + 28 * q^51 + 18 * q^52 + 2 * q^53 - 8 * q^54 - 8 * q^56 - 24 * q^57 - 6 * q^58 - 12 * q^59 - 8 * q^60 - 10 * q^61 - 16 * q^62 - 24 * q^63 + 7 * q^64 + 8 * q^66 + 20 * q^67 + 11 * q^68 - 32 * q^69 + 16 * q^71 - 9 * q^72 - 34 * q^73 + 22 * q^74 - 12 * q^75 + 12 * q^76 + 8 * q^77 - 8 * q^78 + 8 * q^79 + 2 * q^80 + 9 * q^81 + 10 * q^82 + 12 * q^83 + 32 * q^84 + 2 * q^85 + 4 * q^86 + 16 * q^87 + 12 * q^88 + 10 * q^89 - 2 * q^90 - 8 * q^91 - 32 * q^92 + 24 * q^93 - 24 * q^94 - 20 * q^96 + 26 * q^97 - 9 * q^98 - 4 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)

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
17.2.a	\(\chi_{17}(1, \cdot)\)	17.2.a.a	1	1
17.2.b	\(\chi_{17}(16, \cdot)\)	None	0	1
17.2.c	\(\chi_{17}(4, \cdot)\)	None	0	2
17.2.d	\(\chi_{17}(2, \cdot)\)	17.2.d.a	4	4