Space of modular forms of level 22 and weight 4

• Label: 22.4
• Level: 22
• Weight: 4
• Dimension: 15
• Nonzero newspaces: 2
• Newform subspaces: 5
• Sturm bound: 120
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 22 = 2 \cdot 11 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 5 \)
Sturm bound:			\(120\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(22))\).

	Total	New	Old
Modular forms	55	15	40
Cusp forms	35	15	20
Eisenstein series	20	0	20

Trace form

15 * q + 50 * q^6 + 20 * q^7 - 160 * q^9 - 100 * q^10 - 100 * q^11 - 80 * q^12 - 40 * q^13 + 20 * q^14 + 410 * q^15 + 310 * q^17 + 230 * q^18 - 225 * q^19 - 420 * q^21 + 390 * q^23 + 200 * q^24 + 300 * q^25 + 200 * q^26 + 75 * q^27 - 120 * q^28 - 250 * q^29 - 780 * q^30 + 90 * q^31 - 160 * q^32 - 1265 * q^33 - 600 * q^34 - 1010 * q^35 - 100 * q^36 - 240 * q^37 - 60 * q^38 - 160 * q^39 + 240 * q^40 + 830 * q^41 + 2180 * q^42 + 2690 * q^43 + 1060 * q^44 + 1910 * q^45 + 360 * q^46 - 250 * q^47 - 1330 * q^49 - 680 * q^50 - 695 * q^51 - 960 * q^52 + 260 * q^53 - 2160 * q^54 - 370 * q^55 - 945 * q^57 - 1680 * q^58 - 1825 * q^59 - 480 * q^60 + 260 * q^61 + 1380 * q^62 + 1720 * q^63 + 760 * q^65 + 2920 * q^66 + 820 * q^67 + 1240 * q^68 + 840 * q^70 - 3240 * q^71 - 1120 * q^72 - 870 * q^73 - 1400 * q^74 - 5045 * q^75 - 760 * q^76 + 630 * q^77 - 2960 * q^78 + 240 * q^79 - 640 * q^80 + 2505 * q^81 + 1690 * q^82 + 4445 * q^83 + 1840 * q^84 + 2420 * q^85 + 2450 * q^86 + 3400 * q^87 + 560 * q^88 + 350 * q^89 + 2940 * q^90 + 3830 * q^91 - 1680 * q^92 + 6230 * q^93 - 1600 * q^94 - 2200 * q^95 - 3345 * q^97 - 4410 * q^98 - 7790 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(22))\)

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
22.4.a	\(\chi_{22}(1, \cdot)\)	22.4.a.a	1	1
		22.4.a.b	1
		22.4.a.c	1
22.4.c	\(\chi_{22}(3, \cdot)\)	22.4.c.a	4	4
		22.4.c.b	8

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(22))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(22)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 2}\)