Space of modular forms of level 275 and weight 6

• Label: 275.6
• Level: 275
• Weight: 6
• Dimension: 13410
• Nonzero newspaces: 21
• Sturm bound: 36000
• Trace bound: 6

Defining parameters

Level:	\( N \)	=	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 21 \)
Sturm bound:			\(36000\)
Trace bound:			\(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(275))\).

	Total	New	Old
Modular forms	15280	13778	1502
Cusp forms	14720	13410	1310
Eisenstein series	560	368	192

Trace form

13410 * q - 37 * q^2 - 61 * q^3 - 253 * q^4 - 190 * q^5 + 935 * q^6 + 1018 * q^7 - 365 * q^8 - 2727 * q^9 - 840 * q^10 + 180 * q^11 + 18 * q^12 + 1604 * q^13 + 4164 * q^14 + 2380 * q^15 + 8775 * q^16 - 1182 * q^17 - 20856 * q^18 - 17360 * q^19 - 20580 * q^20 - 23270 * q^21 - 3777 * q^22 + 20039 * q^23 + 90745 * q^24 + 37950 * q^25 + 56620 * q^26 + 35765 * q^27 - 25634 * q^28 - 93260 * q^29 - 107740 * q^30 - 28945 * q^31 - 127452 * q^32 - 48861 * q^33 + 66494 * q^34 + 80680 * q^35 + 187380 * q^36 + 96323 * q^37 + 206340 * q^38 - 6984 * q^39 - 159080 * q^40 - 133380 * q^41 - 176654 * q^42 - 109066 * q^43 - 350688 * q^44 - 105530 * q^45 - 391230 * q^46 - 161092 * q^47 + 140224 * q^48 + 336512 * q^49 + 533300 * q^50 + 408830 * q^51 + 790278 * q^52 + 469424 * q^53 + 957810 * q^54 + 137670 * q^55 + 487860 * q^56 - 320380 * q^57 - 340660 * q^58 - 306975 * q^59 - 448500 * q^60 - 423180 * q^61 - 968834 * q^62 - 1148536 * q^63 - 1879373 * q^64 - 556150 * q^65 - 587030 * q^66 - 185167 * q^67 + 217406 * q^68 + 991311 * q^69 + 902260 * q^70 + 438485 * q^71 + 1525675 * q^72 + 269344 * q^73 + 766414 * q^74 + 621500 * q^75 + 984310 * q^76 + 651198 * q^77 + 931828 * q^78 + 571770 * q^79 - 4060 * q^80 - 555940 * q^81 + 103501 * q^82 - 472026 * q^83 - 1482556 * q^84 - 1362410 * q^85 - 1705545 * q^86 - 2213620 * q^87 - 1437935 * q^88 - 1085335 * q^89 - 327920 * q^90 + 1468400 * q^91 + 3045798 * q^92 + 1135573 * q^93 - 41786 * q^94 + 174380 * q^95 - 5011620 * q^96 - 424387 * q^97 - 1402624 * q^98 - 2144257 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(275))\)

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
275.6.a	\(\chi_{275}(1, \cdot)\)	275.6.a.a	1	1
		275.6.a.b	3
		275.6.a.c	3
		275.6.a.d	4
		275.6.a.e	5
		275.6.a.f	6
		275.6.a.g	8
		275.6.a.h	8
		275.6.a.i	8
		275.6.a.j	8
		275.6.a.k	10
		275.6.a.l	14
275.6.b	\(\chi_{275}(199, \cdot)\)	275.6.b.a	2	1
		275.6.b.b	6
		275.6.b.c	6
		275.6.b.d	8
		275.6.b.e	10
		275.6.b.f	12
		275.6.b.g	16
		275.6.b.h	16
275.6.e	\(\chi_{275}(32, \cdot)\)	n/a	176	2
275.6.g	\(\chi_{275}(16, \cdot)\)	n/a	592	4
275.6.h	\(\chi_{275}(26, \cdot)\)	n/a	368	4
275.6.i	\(\chi_{275}(56, \cdot)\)	n/a	504	4
275.6.j	\(\chi_{275}(81, \cdot)\)	n/a	592	4
275.6.k	\(\chi_{275}(36, \cdot)\)	n/a	592	4
275.6.l	\(\chi_{275}(31, \cdot)\)	n/a	592	4
275.6.n	\(\chi_{275}(104, \cdot)\)	n/a	592	4
275.6.t	\(\chi_{275}(14, \cdot)\)	n/a	592	4
275.6.y	\(\chi_{275}(34, \cdot)\)	n/a	496	4
275.6.z	\(\chi_{275}(49, \cdot)\)	n/a	352	4
275.6.ba	\(\chi_{275}(4, \cdot)\)	n/a	592	4
275.6.bb	\(\chi_{275}(9, \cdot)\)	n/a	592	4
275.6.bf	\(\chi_{275}(28, \cdot)\)	n/a	1184	8
275.6.bg	\(\chi_{275}(13, \cdot)\)	n/a	1184	8
275.6.bl	\(\chi_{275}(17, \cdot)\)	n/a	1184	8
275.6.bm	\(\chi_{275}(7, \cdot)\)	n/a	704	8
275.6.bn	\(\chi_{275}(2, \cdot)\)	n/a	1184	8
275.6.bo	\(\chi_{275}(87, \cdot)\)	n/a	1184	8

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(275))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(275)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 2}\)