Space of modular forms of level 55 and weight 4

• Label: 55.4
• Level: 55
• Weight: 4
• Dimension: 298
• Nonzero newspaces: 6
• Newform subspaces: 12
• Sturm bound: 960
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 55 = 5 \cdot 11 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 12 \)
Sturm bound:			\(960\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(55))\).

	Total	New	Old
Modular forms	400	354	46
Cusp forms	320	298	22
Eisenstein series	80	56	24

Trace form

298 * q - 2 * q^2 - 14 * q^3 - 26 * q^4 - 5 * q^5 + 86 * q^6 - 2 * q^7 - 90 * q^8 - 124 * q^9 - 150 * q^10 - 162 * q^11 - 372 * q^12 + 26 * q^13 + 428 * q^14 + 315 * q^15 + 858 * q^16 + 238 * q^17 - 184 * q^18 - 660 * q^19 - 370 * q^20 - 884 * q^21 - 1142 * q^22 + 336 * q^23 + 370 * q^24 - 5 * q^25 + 16 * q^26 + 400 * q^27 + 224 * q^28 + 190 * q^29 + 280 * q^30 + 966 * q^31 - 972 * q^32 + 336 * q^33 + 868 * q^34 - 25 * q^35 + 248 * q^36 - 822 * q^37 + 20 * q^38 - 1398 * q^39 - 1340 * q^40 - 1094 * q^41 - 4064 * q^42 - 2604 * q^43 - 2516 * q^44 - 3310 * q^45 - 3884 * q^46 - 282 * q^47 - 684 * q^48 + 1024 * q^49 + 2190 * q^50 + 4036 * q^51 + 10568 * q^52 + 7066 * q^53 + 14220 * q^54 + 6065 * q^55 + 11120 * q^56 + 6240 * q^57 + 3900 * q^58 - 1600 * q^59 + 2280 * q^60 + 1326 * q^61 - 6224 * q^62 - 1904 * q^63 - 6146 * q^64 - 4670 * q^65 - 8624 * q^66 - 8092 * q^67 - 13376 * q^68 - 7788 * q^69 - 7840 * q^70 - 1794 * q^71 - 4690 * q^72 + 6846 * q^73 + 5048 * q^74 - 65 * q^75 - 2020 * q^76 + 4258 * q^77 + 2912 * q^78 - 130 * q^79 + 2800 * q^80 + 1758 * q^81 + 6126 * q^82 - 1624 * q^83 + 148 * q^84 - 2595 * q^85 + 1686 * q^86 - 6840 * q^87 - 9370 * q^88 - 3620 * q^89 - 13530 * q^90 - 11734 * q^91 - 13492 * q^92 - 13718 * q^93 - 21892 * q^94 - 8735 * q^95 - 22104 * q^96 - 8132 * q^97 - 11276 * q^98 - 2714 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(55))\)

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
55.4.a	\(\chi_{55}(1, \cdot)\)	55.4.a.a	1	1
		55.4.a.b	2
		55.4.a.c	3
		55.4.a.d	4
55.4.b	\(\chi_{55}(34, \cdot)\)	55.4.b.a	6	1
		55.4.b.b	10
55.4.e	\(\chi_{55}(32, \cdot)\)	55.4.e.a	4	2
		55.4.e.b	28
55.4.g	\(\chi_{55}(16, \cdot)\)	55.4.g.a	24	4
		55.4.g.b	24
55.4.j	\(\chi_{55}(4, \cdot)\)	55.4.j.a	64	4
55.4.l	\(\chi_{55}(2, \cdot)\)	55.4.l.a	128	8

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(55))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(55)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 2}\)