Space of modular forms of level 10 and weight 20

• Label: 10.20
• Level: 10
• Weight: 20
• Dimension: 15
• Nonzero newspaces: 2
• Newform subspaces: 5
• Sturm bound: 120
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	=	\( 20 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 5 \)
Sturm bound:			\(120\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{20}(\Gamma_1(10))\).

	Total	New	Old
Modular forms	61	15	46
Cusp forms	53	15	38
Eisenstein series	8	0	8

Trace form

15 * q + 512 * q^2 + 70372 * q^3 - 1310720 * q^4 + 4855795 * q^5 + 46888960 * q^6 - 272909624 * q^7 + 134217728 * q^8 - 8812644985 * q^9 + 997470720 * q^10 - 26607658820 * q^11 + 18447597568 * q^12 + 42687059302 * q^13 - 20729589760 * q^14 + 370190174980 * q^15 + 1030792151040 * q^16 - 130413305574 * q^17 + 78566050304 * q^18 - 3905876173100 * q^19 - 248917524480 * q^20 - 8820511958720 * q^21 + 3580788086784 * q^22 + 2244987950952 * q^23 + 153008209920 * q^24 + 38321062765775 * q^25 + 119589145000960 * q^26 + 18146233127800 * q^27 - 71541620473856 * q^28 + 395253733936650 * q^29 - 371364829624320 * q^30 - 551627017935520 * q^31 + 35184372088832 * q^32 + 326638787488704 * q^33 - 1037641635036160 * q^34 + 1772168076715160 * q^35 + 2260956598763520 * q^36 - 755742421616594 * q^37 + 2989779870791680 * q^38 - 4836530111467720 * q^39 + 262807035576320 * q^40 + 548544587281630 * q^41 + 356527902244864 * q^42 - 5890433108424788 * q^43 - 5420405767536640 * q^44 - 9382913543872365 * q^45 - 3924731761418240 * q^46 + 4064006442579936 * q^47 + 4835927016865792 * q^48 - 31531799790655965 * q^49 + 16805040218022400 * q^50 + 65380049380858280 * q^51 + 11190156473663488 * q^52 + 9595387533001662 * q^53 + 3217011198259200 * q^54 - 59245731323266660 * q^55 + 30997240684216320 * q^56 + 76710950311905680 * q^57 - 28210833504875520 * q^58 - 539347154135593700 * q^59 - 20927165229957120 * q^60 + 411752734958754930 * q^61 + 207032923877453824 * q^62 + 57309083325363992 * q^63 - 90071992547409920 * q^64 - 634777630892667770 * q^65 + 1347896509150289920 * q^66 + 1131032827584999556 * q^67 - 34187065576390656 * q^68 - 1431980104985523920 * q^69 - 1038334441147965440 * q^70 + 2499025516465519080 * q^71 + 20595618690891776 * q^72 - 2364737054355928958 * q^73 - 1645862253804712960 * q^74 - 3612886007445265900 * q^75 + 1176528355144499200 * q^76 + 3133800838977636432 * q^77 - 1613105060298678272 * q^78 - 2524300752819825200 * q^79 + 333687691537285120 * q^80 + 9604007518851591015 * q^81 + 295060066566902784 * q^82 - 235062914463794748 * q^83 - 2049458407672381440 * q^84 - 3471625342709934790 * q^85 + 2667174902793922560 * q^86 + 4440506494908073080 * q^87 + 938682112221904896 * q^88 - 13724156288004191050 * q^89 + 207920525646236160 * q^90 + 4832562148803004880 * q^91 + 588510121414361088 * q^92 - 1754715828918044656 * q^93 - 8010947760089538560 * q^94 - 12618921692788223900 * q^95 + 3222184795895234560 * q^96 + 17503635495991682266 * q^97 - 190754708351061504 * q^98 + 68537366498451907580 * q^99

Decomposition of \(S_{20}^{\mathrm{new}}(\Gamma_1(10))\)

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
10.20.a	\(\chi_{10}(1, \cdot)\)	10.20.a.a	1	1
		10.20.a.b	1
		10.20.a.c	1
		10.20.a.d	2
10.20.b	\(\chi_{10}(9, \cdot)\)	10.20.b.a	10	1

Decomposition of \(S_{20}^{\mathrm{old}}(\Gamma_1(10))\) into lower level spaces

\( S_{20}^{\mathrm{old}}(\Gamma_1(10)) \cong \) \(S_{20}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 1}\)