Space of modular forms of level 155 and weight 7

• Label: 155.7
• Level: 155
• Weight: 7
• Dimension: 5182
• Nonzero newspaces: 12
• Sturm bound: 13440
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 155 = 5 \cdot 31 \)
Weight:	\( k \)	=	\( 7 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(13440\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(155))\).

	Total	New	Old
Modular forms	5880	5354	526
Cusp forms	5640	5182	458
Eisenstein series	240	172	68

Trace form

5182 * q - 10 * q^2 - 90 * q^3 - 30 * q^4 + 95 * q^5 + 1014 * q^6 - 1130 * q^7 - 3750 * q^8 - 30 * q^9 + 8695 * q^10 + 2014 * q^11 - 6990 * q^12 - 3950 * q^13 - 30 * q^14 + 135 * q^15 + 1462 * q^16 + 6530 * q^17 + 1710 * q^18 - 30 * q^19 - 40725 * q^20 - 104946 * q^21 + 95330 * q^22 + 187190 * q^23 + 311010 * q^24 - 60845 * q^25 - 237026 * q^26 - 412590 * q^27 - 604750 * q^28 - 144510 * q^29 + 101220 * q^30 + 198682 * q^31 + 1024820 * q^32 + 344250 * q^33 + 743010 * q^34 + 169895 * q^35 + 81582 * q^36 - 762470 * q^37 - 1060110 * q^38 - 952590 * q^39 - 499845 * q^40 + 374974 * q^41 + 1385250 * q^42 + 799270 * q^43 - 30 * q^44 - 156465 * q^45 - 646666 * q^46 - 1690 * q^47 - 3390960 * q^48 + 205170 * q^49 + 2105330 * q^50 + 5018934 * q^51 + 3282820 * q^52 + 560810 * q^53 - 1305180 * q^54 - 1823725 * q^55 - 6919200 * q^56 - 4967310 * q^57 - 3984300 * q^58 - 1141830 * q^59 - 3617790 * q^60 + 221984 * q^61 + 2641790 * q^62 + 5939400 * q^63 + 5436990 * q^64 + 3970595 * q^65 + 16874808 * q^66 + 2135230 * q^67 + 2777560 * q^68 + 1029570 * q^69 - 1457490 * q^70 - 6552866 * q^71 - 18696600 * q^72 - 4941110 * q^73 - 9818280 * q^74 - 7042965 * q^75 - 4922160 * q^76 + 6447370 * q^77 + 28518900 * q^78 + 5569170 * q^79 + 13082195 * q^80 + 7691142 * q^81 - 1956190 * q^82 - 1708810 * q^83 - 10828830 * q^84 - 424925 * q^85 - 18022346 * q^86 - 7252350 * q^87 - 25337310 * q^88 - 9288030 * q^89 - 10140960 * q^90 - 5445586 * q^91 + 5105300 * q^92 + 5693550 * q^93 + 6004740 * q^94 + 6719715 * q^95 + 32494164 * q^96 + 12567610 * q^97 + 38336950 * q^98 + 13019970 * q^99

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(155))\)

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
155.7.c	\(\chi_{155}(154, \cdot)\)	155.7.c.a	2	1
		155.7.c.b	2
		155.7.c.c	2
		155.7.c.d	4
		155.7.c.e	84
155.7.d	\(\chi_{155}(61, \cdot)\)	155.7.d.a	64	1
155.7.g	\(\chi_{155}(32, \cdot)\)	n/a	180	2
155.7.i	\(\chi_{155}(99, \cdot)\)	n/a	188	2
155.7.k	\(\chi_{155}(6, \cdot)\)	n/a	128	2
155.7.l	\(\chi_{155}(46, \cdot)\)	n/a	256	4
155.7.m	\(\chi_{155}(29, \cdot)\)	n/a	376	4
155.7.o	\(\chi_{155}(67, \cdot)\)	n/a	376	4
155.7.s	\(\chi_{155}(2, \cdot)\)	n/a	752	8
155.7.t	\(\chi_{155}(11, \cdot)\)	n/a	512	8
155.7.v	\(\chi_{155}(24, \cdot)\)	n/a	752	8
155.7.w	\(\chi_{155}(7, \cdot)\)	n/a	1504	16

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(155))\) into lower level spaces

\( S_{7}^{\mathrm{old}}(\Gamma_1(155)) \cong \) \(S_{7}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 2}\)