Space of modular forms of level 44 and weight 4

• Label: 44.4
• Level: 44
• Weight: 4
• Dimension: 95
• Nonzero newspaces: 4
• Newform subspaces: 5
• Sturm bound: 480
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 44 = 2^{2} \cdot 11 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 5 \)
Sturm bound:			\(480\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(44))\).

	Total	New	Old
Modular forms	205	115	90
Cusp forms	155	95	60
Eisenstein series	50	20	30

Trace form

95 * q - 5 * q^2 - 5 * q^4 - 10 * q^5 - 5 * q^6 - 10 * q^7 - 5 * q^8 + 70 * q^9 + 50 * q^11 - 10 * q^12 + 10 * q^13 + 170 * q^14 + 110 * q^15 + 175 * q^16 - 180 * q^17 - 230 * q^18 - 225 * q^19 - 480 * q^20 - 420 * q^21 - 635 * q^22 - 480 * q^23 - 455 * q^24 - 430 * q^25 - 30 * q^26 + 165 * q^27 + 520 * q^28 + 640 * q^29 + 880 * q^30 + 990 * q^31 + 1795 * q^33 - 950 * q^34 + 940 * q^35 - 390 * q^36 + 70 * q^37 + 320 * q^38 - 610 * q^39 + 1080 * q^40 - 1720 * q^41 + 2290 * q^42 - 1990 * q^43 + 1500 * q^44 - 4050 * q^45 + 1330 * q^46 - 340 * q^47 + 1260 * q^48 + 200 * q^49 + 655 * q^50 + 1825 * q^51 + 1610 * q^52 + 4470 * q^53 + 2870 * q^55 - 1020 * q^56 + 3315 * q^57 - 1200 * q^58 - 295 * q^59 - 3080 * q^60 - 1490 * q^61 - 3980 * q^62 - 4400 * q^63 - 3785 * q^64 - 4280 * q^65 - 4230 * q^66 - 4190 * q^67 - 3840 * q^68 - 2920 * q^69 - 4420 * q^70 - 480 * q^71 - 5555 * q^72 - 460 * q^73 - 1890 * q^74 + 3835 * q^75 + 3580 * q^77 + 4360 * q^78 + 3390 * q^79 + 7500 * q^80 + 4325 * q^81 + 6985 * q^82 - 415 * q^83 + 6530 * q^84 - 410 * q^85 + 3355 * q^86 - 1700 * q^87 + 6955 * q^88 + 230 * q^89 + 10080 * q^90 + 1580 * q^91 + 7920 * q^92 + 4780 * q^93 + 7280 * q^94 + 4130 * q^95 + 5720 * q^96 + 3755 * q^97 + 3970 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(44))\)

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
44.4.a	\(\chi_{44}(1, \cdot)\)	44.4.a.a	1	1
		44.4.a.b	2
44.4.c	\(\chi_{44}(43, \cdot)\)	44.4.c.a	16	1
44.4.e	\(\chi_{44}(5, \cdot)\)	44.4.e.a	12	4
44.4.g	\(\chi_{44}(7, \cdot)\)	44.4.g.a	64	4

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(44))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(44)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 2}\)