Space of modular forms of level 25 and weight 16

• Label: 25.16
• Level: 25
• Weight: 16
• Dimension: 336
• Nonzero newspaces: 4
• Sturm bound: 800
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 25 = 5^{2} \)
Weight:	\( k \)	=	\( 16 \)
Nonzero newspaces:			\( 4 \)
Sturm bound:			\(800\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{16}(\Gamma_1(25))\).

	Total	New	Old
Modular forms	389	357	32
Cusp forms	361	336	25
Eisenstein series	28	21	7

Trace form

336 * q - 46 * q^2 - 482 * q^3 - 84418 * q^4 + 264355 * q^5 - 638738 * q^6 + 184834 * q^7 + 6197030 * q^8 - 9658647 * q^9 + 61549680 * q^10 - 87258318 * q^11 - 377734026 * q^12 + 1066336688 * q^13 - 1009919866 * q^14 + 15627120 * q^15 - 5610154354 * q^16 - 3110421476 * q^17 + 6776021218 * q^18 - 16953922990 * q^19 + 34457130650 * q^20 + 45465270342 * q^21 - 89991924762 * q^22 - 29493489102 * q^23 + 240590612140 * q^24 + 22107831985 * q^25 - 99157876788 * q^26 + 15546532690 * q^27 + 965462598742 * q^28 - 709508455920 * q^29 - 770949440570 * q^30 - 32338687618 * q^31 + 2950171486134 * q^32 - 544883536314 * q^33 - 4456855963026 * q^34 - 101416073080 * q^35 + 4926744873846 * q^36 + 2962981141529 * q^37 - 9539148923140 * q^38 - 9327050385234 * q^39 + 7347038249740 * q^40 + 5699365955632 * q^41 + 6953378033338 * q^42 + 4512194194878 * q^43 - 23311317930296 * q^44 - 9765590765185 * q^45 + 11173787636682 * q^46 + 25641267552994 * q^47 + 16048460757588 * q^48 - 36121361634408 * q^49 + 25135480266050 * q^50 + 52712771836392 * q^51 + 6487826553124 * q^52 - 79402466025967 * q^53 - 28798462532800 * q^54 + 41214265811230 * q^55 + 193504197304210 * q^56 + 11710501324550 * q^57 - 278170658674780 * q^58 - 132351236550690 * q^59 + 191018468820290 * q^60 + 26986261743332 * q^61 + 245934834116448 * q^62 - 35334573756442 * q^63 - 153094634465768 * q^64 - 376368765658735 * q^65 - 212508435264466 * q^66 - 29573408459786 * q^67 + 823794215104742 * q^68 + 539703600837046 * q^69 - 580354158258850 * q^70 - 475699858440418 * q^71 - 1227099623351880 * q^72 + 286749060754388 * q^73 + 2725998687046644 * q^74 + 826212780117460 * q^75 - 1715128675963580 * q^76 - 1709445175110282 * q^77 - 1070611990455064 * q^78 + 927372070763110 * q^79 + 1565264979166790 * q^80 - 1889600464359759 * q^81 + 1586072995721878 * q^82 - 1080551884347102 * q^83 + 162835358520614 * q^84 + 2068473543530715 * q^85 - 377596453272198 * q^86 - 3524090150749390 * q^87 + 286353719793470 * q^88 - 847970631089505 * q^89 + 29999000778510 * q^90 - 354457033668098 * q^91 + 10837308328388514 * q^92 - 173657072014394 * q^93 - 7425883444735866 * q^94 - 5382840752783990 * q^95 - 1267675699390678 * q^96 + 1618943245685544 * q^97 + 2913160782562942 * q^98 + 7997399568934536 * q^99

Decomposition of \(S_{16}^{\mathrm{new}}(\Gamma_1(25))\)

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
25.16.a	\(\chi_{25}(1, \cdot)\)	25.16.a.a	1	1
		25.16.a.b	2
		25.16.a.c	3
		25.16.a.d	5
		25.16.a.e	5
		25.16.a.f	6
25.16.b	\(\chi_{25}(24, \cdot)\)	25.16.b.a	2	1
		25.16.b.b	4
		25.16.b.c	6
		25.16.b.d	10
25.16.d	\(\chi_{25}(6, \cdot)\)	n/a	148	4
25.16.e	\(\chi_{25}(4, \cdot)\)	n/a	144	4

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

Decomposition of \(S_{16}^{\mathrm{old}}(\Gamma_1(25))\) into lower level spaces

\( S_{16}^{\mathrm{old}}(\Gamma_1(25)) \cong \) \(S_{16}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)