Space of modular forms of level 10 and weight 32

• Label: 10.32
• Level: 10
• Weight: 32
• Dimension: 25
• Nonzero newspaces: 2
• Newform subspaces: 5
• Sturm bound: 192
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	=	\( 32 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 5 \)
Sturm bound:			\(192\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{32}(\Gamma_1(10))\).

	Total	New	Old
Modular forms	97	25	72
Cusp forms	89	25	64
Eisenstein series	8	0	8

Trace form

25 * q + 32768 * q^2 + 62917228 * q^3 - 7516192768 * q^4 - 45002762995 * q^5 + 568547737600 * q^6 + 40452679234344 * q^7 + 35184372088832 * q^8 - 3946256568750259 * q^9 - 210191519416320 * q^10 - 3424434768752700 * q^11 + 67556859153743872 * q^12 + 18506974808973798 * q^13 - 1681561298718162944 * q^14 + 432050940465138220 * q^15 + 28823037615171174400 * q^16 + 512816064594633474 * q^17 + 82038791749239996416 * q^18 - 374147342482092261060 * q^19 + 113857348823291002880 * q^20 + 473177156497664642800 * q^21 + 61601576950766370816 * q^22 - 815148792745897217832 * q^23 + 563154163516915580928 * q^24 + 10886498475052418129025 * q^25 + 23507520482163653017600 * q^26 - 47153562783358673669480 * q^27 + 43435733586771450003456 * q^28 - 10708479114028895011290 * q^29 + 55698898904187605483520 * q^30 - 169185864105790471947200 * q^31 + 37778931862957161709568 * q^32 + 666451202483194012968336 * q^33 - 1200241007611384978407424 * q^34 + 2662523739573104441924440 * q^35 + 5898609740702427591475200 * q^36 - 3217833821465536391118066 * q^37 - 4007743966567191033282560 * q^38 - 10929896489880125504258008 * q^39 + 2373175073447410852167680 * q^40 + 46160346867360805309525050 * q^41 - 48350057258151359858868224 * q^42 + 72759356030870164088278308 * q^43 - 69238967129373143797334016 * q^44 + 179452712229531726530602065 * q^45 + 47392348023748394097049600 * q^46 - 252920624458381337032724736 * q^47 + 72538625171452041550102528 * q^48 - 919684436233018591673298351 * q^49 + 228044524566929488754278400 * q^50 - 67600503009662159297756200 * q^51 + 19871712888109577432727552 * q^52 + 904524338277503938631511678 * q^53 + 198610097032095123241697280 * q^54 - 3564302426927526831399444940 * q^55 + 315802397550315589284659200 * q^56 + 2554582325203459139142212240 * q^57 - 5888848454979048632756797440 * q^58 + 26973249727133362857661734420 * q^59 - 5248561617867952920754913280 * q^60 - 12717763755513865854920089450 * q^61 + 6147867149415889064795570176 * q^62 - 11795411115036385449220253272 * q^63 - 8665580274997661924293869568 * q^64 + 8650781110164925299595090270 * q^65 + 87385520458107568593711923200 * q^66 - 25607325075061211743465970676 * q^67 + 550632056574343566984216576 * q^68 + 51861379654805735488897213072 * q^69 - 65002250105504971270380584960 * q^70 - 249431195412392337507716596200 * q^71 + 88088481891585104365469302784 * q^72 + 84505411594301660500923972618 * q^73 - 155409420966784640376174608384 * q^74 + 543647663349628429965688321100 * q^75 + 222925872952312026875559936000 * q^76 + 24709739675746271361232508928 * q^77 - 206011860783189316397696811008 * q^78 - 877794059087379491513772401040 * q^79 - 51884653223660735115160453120 * q^80 - 691530854959984457834650200975 * q^81 - 76784047850925072269297516544 * q^82 + 2602128461163099209651437067388 * q^83 - 1934315307932995765382022168576 * q^84 - 60843563085064955688840811510 * q^85 + 3117611231827162550012664217600 * q^86 + 681575015886860063728937546760 * q^87 + 66144189596392241197832208384 * q^88 + 3951982432484435708914874735130 * q^89 - 5536424903995451478884958044160 * q^90 - 1016302571064276298720444081200 * q^91 - 875259351554377647191457005568 * q^92 - 5778120217738832488013252891104 * q^93 + 15255150006693209616055846567936 * q^94 - 3721283275012353925450214402900 * q^95 + 655490913074610825674201497600 * q^96 - 13461378010917022697870537651886 * q^97 - 4606577489797374657476047896576 * q^98 - 23017815535336717420011762184108 * q^99

Decomposition of \(S_{32}^{\mathrm{new}}(\Gamma_1(10))\)

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
10.32.a	\(\chi_{10}(1, \cdot)\)	10.32.a.a	2	1
		10.32.a.b	2
		10.32.a.c	2
		10.32.a.d	3
10.32.b	\(\chi_{10}(9, \cdot)\)	10.32.b.a	16	1

Decomposition of \(S_{32}^{\mathrm{old}}(\Gamma_1(10))\) into lower level spaces

\( S_{32}^{\mathrm{old}}(\Gamma_1(10)) \cong \) \(S_{32}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{32}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{32}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{32}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 1}\)