Space of modular forms of level 19 and weight 4

• Label: 19.4
• Level: 19
• Weight: 4
• Dimension: 36
• Nonzero newspaces: 3
• Newform subspaces: 5
• Sturm bound: 120
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 19 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 3 \)
Newform subspaces:			\( 5 \)
Sturm bound:			\(120\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(19))\).

	Total	New	Old
Modular forms	54	52	2
Cusp forms	36	36	0
Eisenstein series	18	16	2

Trace form

36 * 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 - 297 * q^12 - 153 * q^13 - 45 * q^14 + 99 * q^15 + 423 * q^16 + 135 * q^17 + 468 * q^18 + 369 * q^19 + 558 * q^20 + 243 * q^21 + 153 * q^22 - 27 * q^23 - 441 * q^24 - 441 * q^25 - 693 * q^26 - 1314 * q^27 - 2304 * q^28 - 639 * q^29 - 1206 * q^30 - 99 * q^31 + 306 * q^32 + 909 * q^33 + 1116 * q^34 + 1107 * q^35 + 3069 * q^36 + 648 * q^37 + 2322 * q^38 + 1872 * q^39 + 1872 * q^40 + 441 * q^41 + 1521 * q^42 - 135 * q^43 - 2934 * q^44 - 3087 * q^45 - 3528 * q^46 - 1881 * q^47 - 5616 * q^48 - 1719 * q^49 - 2214 * q^50 - 144 * q^51 + 2367 * q^52 + 1575 * q^53 + 2448 * q^54 + 1935 * q^55 + 6030 * q^56 + 2511 * q^57 + 1926 * q^58 + 2241 * q^59 + 1530 * q^60 - 2763 * q^61 - 3420 * q^62 - 3393 * q^63 - 4113 * q^64 - 2619 * q^65 - 3537 * q^66 - 927 * q^67 - 3600 * q^68 - 333 * q^69 + 315 * q^70 - 2187 * q^71 + 2952 * q^72 + 4932 * q^73 + 5175 * q^74 + 6282 * q^75 + 6741 * q^76 + 4644 * q^77 - 279 * q^78 + 2655 * q^79 - 2889 * q^80 + 468 * q^81 + 2214 * q^82 - 351 * q^83 - 1413 * q^84 - 945 * q^85 - 1422 * q^86 - 1377 * q^87 - 1161 * q^88 - 4059 * q^89 - 4194 * q^90 - 4977 * q^91 - 2538 * q^92 - 315 * q^93 - 2862 * q^94 - 5715 * q^95 - 666 * q^96 - 3357 * q^97 - 6678 * q^98 - 792 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(19))\)

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
19.4.a	\(\chi_{19}(1, \cdot)\)	19.4.a.a	1	1
		19.4.a.b	3
19.4.c	\(\chi_{19}(7, \cdot)\)	19.4.c.a	4	2
		19.4.c.b	4
19.4.e	\(\chi_{19}(4, \cdot)\)	19.4.e.a	24	6