Space of modular forms of level 19 and weight 2

• Label: 19.2
• Level: 19
• Weight: 2
• Dimension: 7
• Nonzero newspaces: 2
• Newform subspaces: 2
• Sturm bound: 60
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 19 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 2 \)
Sturm bound:			\(60\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(19))\).

	Total	New	Old
Modular forms	24	24	0
Cusp forms	7	7	0
Eisenstein series	17	17	0

Trace form

7 * q - 6 * q^2 - 5 * q^3 - 2 * q^4 - 3 * q^5 + 3 * q^6 - q^7 + 6 * q^8 + 4 * q^9 + 9 * q^10 + 3 * q^11 + 7 * q^12 - 7 * q^13 - 3 * q^14 - 3 * q^15 - 14 * q^16 - 6 * q^18 - 11 * q^19 - 12 * q^20 + 2 * q^21 + 6 * q^23 + 15 * q^24 + 4 * q^25 + 15 * q^26 + 10 * q^27 + 8 * q^28 + 3 * q^29 + 5 * q^31 + 9 * q^32 - 15 * q^33 + 3 * q^35 - 26 * q^36 + 2 * q^37 - 15 * q^38 - 16 * q^39 + 15 * q^41 - 3 * q^42 - 4 * q^43 + 3 * q^44 - 12 * q^45 - 18 * q^46 - 6 * q^47 - 11 * q^48 + 9 * q^49 - 15 * q^50 + 9 * q^51 + 23 * q^52 + 9 * q^53 + 30 * q^54 + 27 * q^55 - 6 * q^56 + 22 * q^57 + 36 * q^58 + 6 * q^59 + 6 * q^60 - 13 * q^61 - 12 * q^62 + 11 * q^63 - 20 * q^64 - 24 * q^65 - 9 * q^66 - 34 * q^67 - 9 * q^68 - 12 * q^69 - 9 * q^70 - 12 * q^72 - 19 * q^73 + 15 * q^74 + 22 * q^75 + 34 * q^76 - 21 * q^77 + 15 * q^78 - 31 * q^79 + 15 * q^80 - 5 * q^81 - 54 * q^82 + 12 * q^83 - q^84 - 9 * q^85 + 24 * q^86 - 33 * q^87 + 9 * q^88 + 18 * q^90 + 19 * q^91 + 42 * q^92 + 17 * q^93 + 18 * q^94 + 42 * q^95 + 18 * q^96 + 26 * q^97 - 9 * q^98 + 12 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)

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
19.2.a	\(\chi_{19}(1, \cdot)\)	19.2.a.a	1	1
19.2.c	\(\chi_{19}(7, \cdot)\)	None	0	2
19.2.e	\(\chi_{19}(4, \cdot)\)	19.2.e.a	6	6