Space of modular forms of level 11 and weight 4

• Label: 11.4
• Level: 11
• Weight: 4
• Dimension: 10
• Nonzero newspaces: 2
• Newform subspaces: 2
• Sturm bound: 40
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 11 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 2 \)
Sturm bound:			\(40\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(11))\).

	Total	New	Old
Modular forms	20	18	2
Cusp forms	10	10	0
Eisenstein series	10	8	2

Trace form

10 * q - 5 * q^2 - 5 * q^3 - 5 * q^4 - 5 * q^5 - 55 * q^6 - 15 * q^7 + 35 * q^8 + 75 * q^9 + 90 * q^10 + 45 * q^11 + 150 * q^12 + 15 * q^13 - 200 * q^14 - 315 * q^15 - 385 * q^16 - 155 * q^17 - 10 * q^18 + 220 * q^19 + 430 * q^20 + 410 * q^21 + 625 * q^22 - 110 * q^23 - 195 * q^24 - 65 * q^25 - 180 * q^26 - 110 * q^27 - 170 * q^28 - 55 * q^29 - 380 * q^30 - 395 * q^31 + 220 * q^32 - 210 * q^33 - 350 * q^34 + 65 * q^35 + 40 * q^36 + 135 * q^37 + 380 * q^38 + 765 * q^39 + 40 * q^40 + 505 * q^41 + 30 * q^42 - 710 * q^43 - 1120 * q^44 + 880 * q^45 + 890 * q^46 + 585 * q^47 + 1420 * q^48 + 985 * q^49 + 85 * q^50 - 410 * q^51 - 1150 * q^52 - 1985 * q^53 - 3210 * q^54 - 1605 * q^55 - 1440 * q^56 - 1410 * q^57 + 1200 * q^58 + 1310 * q^59 + 1700 * q^60 + 315 * q^61 + 2590 * q^62 + 180 * q^63 + 695 * q^64 + 910 * q^65 + 1300 * q^66 + 840 * q^67 + 1350 * q^68 + 920 * q^69 + 140 * q^70 + 465 * q^71 + 175 * q^72 - 2555 * q^73 - 1470 * q^74 - 680 * q^75 + 190 * q^76 - 2235 * q^77 - 1780 * q^78 - 545 * q^79 - 3460 * q^80 - 1320 * q^81 - 2985 * q^82 + 520 * q^83 - 820 * q^84 + 2835 * q^85 + 905 * q^86 + 3510 * q^87 + 4675 * q^88 + 1940 * q^89 - 150 * q^90 + 1415 * q^91 - 2490 * q^92 - 2715 * q^93 - 290 * q^94 + 1635 * q^95 + 300 * q^96 + 850 * q^97 + 1870 * q^98 + 1615 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(11))\)

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
11.4.a	\(\chi_{11}(1, \cdot)\)	11.4.a.a	2	1
11.4.c	\(\chi_{11}(3, \cdot)\)	11.4.c.a	8	4