Space of modular forms of level 1 and weight 20

• Label: 1.20
• Level: 1
• Weight: 20
• Dimension: 1
• Nonzero newspaces: 1
• Newform subspaces: 1
• Sturm bound: 1
• Trace bound: 0

Defining parameters

Level:	\( N \)	=	\( 1 \)
Weight:	\( k \)	=	\( 20 \)
Nonzero newspaces:			\( 1 \)
Newform subspaces:			\( 1 \)
Sturm bound:			\(1\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{20}(\Gamma_1(1))\).

	Total	New	Old
Modular forms	2	2	0
Cusp forms	1	1	0
Eisenstein series	1	1	0

Trace form

q + 456 * q^2 + 50652 * q^3 - 316352 * q^4 - 2377410 * q^5 + 23097312 * q^6 - 16917544 * q^7 - 383331840 * q^8 + 1403363637 * q^9 - 1084098960 * q^10 - 16212108 * q^11 - 16023861504 * q^12 + 50421615062 * q^13 - 7714400064 * q^14 - 120420571320 * q^15 - 8939761664 * q^16 + 225070099506 * q^17 + 639933818472 * q^18 - 1710278572660 * q^19 + 752098408320 * q^20 - 856907438688 * q^21 - 7392721248 * q^22 + 14036534788872 * q^23 - 19416524359680 * q^24 - 13421408020025 * q^25 + 22992256468272 * q^26 + 12212307114840 * q^27 + 5351898879488 * q^28 + 1137835269510 * q^29 - 54911780521920 * q^30 - 104626880141728 * q^31 + 196899752411136 * q^32 - 821175694416 * q^33 + 102631965374736 * q^34 + 40219938281040 * q^35 - 443956893292224 * q^36 - 169392327370594 * q^37 - 779887029132960 * q^38 + 2553955646120424 * q^39 + 911336949734400 * q^40 - 3309984750560838 * q^41 - 390749792041728 * q^42 + 1127913532193492 * q^43 + 5128732790016 * q^44 - 3336370744240170 * q^45 + 6400659863725632 * q^46 + 3498693987674256 * q^47 - 452816807804928 * q^48 - 11112691890381207 * q^49 - 6120162057131400 * q^50 + 11400250680177912 * q^51 - 15950978768093824 * q^52 + 29956294112980302 * q^53 + 5568812044367040 * q^54 + 38542827680280 * q^55 + 6485033269800960 * q^56 - 86629030262374320 * q^57 + 518852882896560 * q^58 + 58391397642732420 * q^59 + 38095288578224640 * q^60 + 23373685132672742 * q^61 - 47709857344627968 * q^62 - 23741466076947528 * q^63 + 94473296862773248 * q^64 - 119872851864549420 * q^65 - 374456116653696 * q^66 - 205102524257382244 * q^67 - 71201376118922112 * q^68 + 710978560125944544 * q^69 + 18340291856154240 * q^70 - 177902341950417768 * q^71 - 537953965160302080 * q^72 + 299853775038660122 * q^73 - 77242901280990864 * q^74 - 679821159030306300 * q^75 + 541050047018136320 * q^76 + 274269050422752 * q^77 + 1164603774630913344 * q^78 - 92227090144007440 * q^79 + 21253478777610240 * q^80 - 1012497699493199799 * q^81 - 1509353046255742128 * q^82 + 1208542823470585932 * q^83 + 271084382043826176 * q^84 - 535083905266559460 * q^85 + 514328570680232352 * q^86 + 57633632071220520 * q^87 + 6214617189918720 * q^88 + 4371201192290304330 * q^89 - 1521385059373517520 * q^90 - 853009891362447728 * q^91 - 4440485853529234944 * q^92 - 5299560732938806656 * q^93 + 1595404458379460736 * q^94 + 4066033381427610600 * q^95 + 9973366259128860672 * q^96 - 635013222218448094 * q^97 - 5067387502013830392 * q^98 - 22751482846316796 * q^99

Decomposition of \(S_{20}^{\mathrm{new}}(\Gamma_1(1))\)

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
1.20.a	\(\chi_{1}(1, \cdot)\)	1.20.a.a	1	1