Space of modular forms of level 19 and weight 5

• Label: 19.5
• Level: 19
• Weight: 5
• Dimension: 51
• Nonzero newspaces: 3
• Newform subspaces: 4
• Sturm bound: 150
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 19 \)
Weight:	\( k \)	=	\( 5 \)
Nonzero newspaces:			\( 3 \)
Newform subspaces:			\( 4 \)
Sturm bound:			\(150\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(19))\).

	Total	New	Old
Modular forms	69	69	0
Cusp forms	51	51	0
Eisenstein series	18	18	0

Trace form

51 * q - 9 * q^2 - 9 * q^3 - 9 * q^4 - 9 * q^5 - 9 * q^6 - 9 * q^7 - 9 * q^8 - 9 * q^9 - 9 * q^10 - 9 * q^11 + 855 * q^12 - 69 * q^13 - 873 * q^14 - 1143 * q^15 - 2025 * q^16 - 306 * q^17 + 768 * q^19 + 2574 * q^20 + 2070 * q^21 + 3015 * q^22 + 936 * q^23 + 2583 * q^24 + 117 * q^25 - 1737 * q^26 + 1215 * q^27 + 786 * q^28 + 855 * q^29 - 4860 * q^30 - 2817 * q^31 - 8784 * q^32 - 10809 * q^33 - 7974 * q^34 - 4761 * q^35 - 6255 * q^36 + 4716 * q^38 + 7974 * q^39 + 13266 * q^40 + 4743 * q^41 + 26541 * q^42 + 14028 * q^43 + 30420 * q^44 + 20430 * q^45 + 7326 * q^46 - 4248 * q^47 - 33462 * q^48 - 17148 * q^49 - 51876 * q^50 - 29178 * q^51 - 23241 * q^52 - 10485 * q^53 - 10512 * q^54 - 3933 * q^55 + 5076 * q^57 + 8046 * q^58 + 14706 * q^59 + 72540 * q^60 + 48531 * q^61 + 54828 * q^62 + 29763 * q^63 + 28239 * q^64 + 3636 * q^65 - 10017 * q^66 - 37326 * q^67 - 44424 * q^68 - 54954 * q^69 - 90333 * q^70 - 51768 * q^71 - 100764 * q^72 - 30306 * q^73 - 10449 * q^74 + 13581 * q^76 + 47637 * q^77 + 97137 * q^78 + 65793 * q^79 + 73503 * q^80 + 64503 * q^81 + 100026 * q^82 + 16002 * q^83 + 11115 * q^84 + 21555 * q^85 + 4230 * q^86 - 37089 * q^87 - 69057 * q^88 - 34272 * q^89 - 102024 * q^90 - 75525 * q^91 - 106254 * q^92 - 87849 * q^93 + 91926 * q^95 + 172854 * q^96 + 50688 * q^97 + 94896 * q^98 + 60507 * q^99

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(19))\)

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
19.5.b	\(\chi_{19}(18, \cdot)\)	19.5.b.a	1	1
		19.5.b.b	4
19.5.d	\(\chi_{19}(8, \cdot)\)	19.5.d.a	10	2
19.5.f	\(\chi_{19}(2, \cdot)\)	19.5.f.a	36	6