Space of modular forms of level 44 and weight 3

• Label: 44.3
• Level: 44
• Weight: 3
• Dimension: 60
• Nonzero newspaces: 4
• Newform subspaces: 4
• Sturm bound: 360
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 44 = 2^{2} \cdot 11 \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 4 \)
Sturm bound:			\(360\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(44))\).

	Total	New	Old
Modular forms	145	76	69
Cusp forms	95	60	35
Eisenstein series	50	16	34

Trace form

60 * q - 5 * q^2 - 5 * q^4 - 10 * q^5 - 5 * q^6 + 15 * q^7 - 5 * q^8 - 10 * q^10 - 5 * q^11 - 10 * q^12 - 25 * q^13 - 40 * q^14 - 110 * q^15 - 105 * q^16 - 85 * q^17 - 80 * q^18 - 30 * q^19 - 30 * q^20 - 20 * q^21 + 25 * q^22 + 65 * q^23 + 85 * q^24 + 140 * q^25 + 120 * q^26 + 165 * q^27 + 170 * q^28 + 115 * q^29 + 220 * q^30 + 110 * q^31 + 100 * q^32 - 185 * q^33 + 170 * q^34 - 155 * q^35 + 320 * q^36 - 300 * q^37 + 120 * q^38 - 185 * q^39 + 100 * q^40 - 205 * q^41 + 30 * q^42 - 40 * q^44 + 190 * q^45 - 90 * q^46 + 145 * q^47 - 280 * q^48 + 295 * q^49 - 375 * q^50 + 150 * q^51 - 490 * q^52 + 165 * q^53 - 890 * q^54 - 100 * q^55 - 720 * q^56 - 180 * q^57 - 360 * q^58 - 285 * q^59 - 480 * q^60 - 155 * q^61 - 230 * q^62 - 110 * q^63 - 65 * q^64 - 20 * q^65 + 60 * q^66 - 25 * q^67 + 190 * q^68 + 265 * q^69 + 540 * q^70 + 340 * q^71 + 895 * q^72 + 335 * q^73 + 950 * q^74 + 390 * q^75 + 870 * q^76 + 555 * q^77 + 1180 * q^78 + 235 * q^79 + 980 * q^80 + 370 * q^81 + 585 * q^82 + 210 * q^83 + 340 * q^84 + 175 * q^85 + 55 * q^86 - 85 * q^88 + 55 * q^89 - 670 * q^90 - 195 * q^91 - 550 * q^92 - 740 * q^93 - 950 * q^94 - 255 * q^95 - 1320 * q^96 - 495 * q^97 - 1220 * q^98 - 540 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(44))\)

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
44.3.b	\(\chi_{44}(23, \cdot)\)	44.3.b.a	10	1
44.3.d	\(\chi_{44}(21, \cdot)\)	44.3.d.a	2	1
44.3.f	\(\chi_{44}(13, \cdot)\)	44.3.f.a	8	4
44.3.h	\(\chi_{44}(3, \cdot)\)	44.3.h.a	40	4

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(44))\) into lower level spaces

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