Space of modular forms of level 19 and weight 13

• Label: 19.13
• Level: 19
• Weight: 13
• Dimension: 171
• Nonzero newspaces: 3
• Newform subspaces: 4
• Sturm bound: 390
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 19 \)
Weight:	\( k \)	=	\( 13 \)
Nonzero newspaces:			\( 3 \)
Newform subspaces:			\( 4 \)
Sturm bound:			\(390\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{13}(\Gamma_1(19))\).

	Total	New	Old
Modular forms	189	189	0
Cusp forms	171	171	0
Eisenstein series	18	18	0

Trace form

171 * 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 - 9 * q^12 - 5100489 * q^13 - 19948041 * q^14 + 57316887 * q^15 - 17031177 * q^16 - 52747209 * q^17 + 223999767 * q^19 + 222953454 * q^20 - 315242937 * q^21 - 606009609 * q^22 + 95301351 * q^23 + 1773674487 * q^24 + 147341367 * q^25 - 1731953673 * q^26 - 407694789 * q^27 + 4198497426 * q^28 + 1729758231 * q^29 - 9745857900 * q^30 - 1766217969 * q^31 + 6764182416 * q^32 + 11688159591 * q^33 - 240742134 * q^34 - 10132266681 * q^35 - 27591887295 * q^36 + 25543505916 * q^38 + 28858432662 * q^39 + 11128084866 * q^40 - 8732869209 * q^41 - 82556879859 * q^42 + 471184551 * q^43 - 36320616684 * q^44 + 131903487495 * q^45 + 92480795406 * q^46 - 57085699329 * q^47 - 304431429654 * q^48 - 14405163129 * q^49 + 300190948524 * q^50 + 31766040171 * q^51 + 43088855031 * q^52 - 67897051209 * q^53 - 183494647440 * q^54 - 97511148873 * q^55 + 146292602391 * q^57 + 181515479022 * q^58 + 177745427991 * q^59 + 52544642940 * q^60 - 484393779729 * q^61 + 34030880316 * q^62 + 210382983351 * q^63 - 274601155761 * q^64 - 262369520289 * q^65 + 317531163231 * q^66 + 314482633911 * q^67 + 331371931896 * q^68 + 413690184999 * q^69 + 186810746787 * q^70 + 363467910951 * q^71 - 834575007420 * q^72 - 1917486602109 * q^73 - 884664375777 * q^74 + 1266286641741 * q^76 + 2219916880422 * q^77 + 207206238177 * q^78 + 1408375748727 * q^79 + 1926574327503 * q^80 - 1752705337581 * q^81 - 5988358353654 * q^82 - 2271590101449 * q^83 - 3544801721397 * q^84 + 2241735299415 * q^85 + 4716483421014 * q^86 + 7363881783351 * q^87 + 4424243143311 * q^88 - 2309877014913 * q^89 - 9455207430024 * q^90 - 5144506975881 * q^91 - 1392442235694 * q^92 + 2527222701231 * q^93 - 5893911540009 * q^95 + 10469396790198 * q^96 + 7076273922711 * q^97 + 14795756449056 * q^98 + 151307974539 * q^99

Decomposition of \(S_{13}^{\mathrm{new}}(\Gamma_1(19))\)

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
19.13.b	\(\chi_{19}(18, \cdot)\)	19.13.b.a	1	1
		19.13.b.b	18
19.13.d	\(\chi_{19}(8, \cdot)\)	19.13.d.a	38	2
19.13.f	\(\chi_{19}(2, \cdot)\)	19.13.f.a	114	6