Space of modular forms of level 10 and weight 34

• Label: 10.34
• Level: 10
• Weight: 34
• Dimension: 27
• Nonzero newspaces: 2
• Newform subspaces: 5
• Sturm bound: 204
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	=	\( 34 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 5 \)
Sturm bound:			\(204\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{34}(\Gamma_1(10))\).

	Total	New	Old
Modular forms	103	27	76
Cusp forms	95	27	68
Eisenstein series	8	0	8

Trace form

27 * q - 65536 * q^2 + 74568256 * q^3 - 21474836480 * q^4 - 147433460545 * q^5 - 15356278341632 * q^6 + 22560918015772 * q^7 - 281474976710656 * q^8 - 16101758754062665 * q^9 - 36218416402595840 * q^10 - 63774850474723476 * q^11 + 320268220839755776 * q^12 - 8874325095364822094 * q^13 - 4343029386342563840 * q^14 - 38908785642656833640 * q^15 + 498062089990157893632 * q^16 + 292948424559249424662 * q^17 + 344984409678544044032 * q^18 - 2012547227397285118100 * q^19 - 677498108623118663680 * q^20 - 1369224973675817563736 * q^21 + 11364797013025828896768 * q^22 + 6370309914738581109876 * q^23 - 31113461425160658616320 * q^24 + 89918258431263204453275 * q^25 - 94091618403651555295232 * q^26 + 2061553675044024442919440 * q^27 + 96898405045477952192512 * q^28 + 2353012367869685335599450 * q^29 + 809602241657898270720 * q^30 - 1004303179924653061901896 * q^31 - 1208925819614629174706176 * q^32 + 32887585740938981039977872 * q^33 - 85043846958714764597002240 * q^34 - 53663459451495556859725820 * q^35 + 168802392657457004723306496 * q^36 - 58155933769018527442357238 * q^37 - 422915893532945301772697600 * q^38 + 971158711935772407168738320 * q^39 + 69657568042059102305648640 * q^40 - 1495662810479023539024019626 * q^41 + 1983383128835802691690037248 * q^42 + 40321834485560811883229176 * q^43 + 494447123832830640877731840 * q^44 - 8362338214986920461880868165 * q^45 + 5793703568213244447493193728 * q^46 + 6076370083323837895466025972 * q^47 + 1375541534454856714547101696 * q^48 + 54533549092526387465823105915 * q^49 - 16376487488698696002818867200 * q^50 - 6039394084254725866782540256 * q^51 - 38114936058663992082588237824 * q^52 - 154273000350213599237533444854 * q^53 + 107015386277012088450121728000 * q^54 - 169162888715252650690451683540 * q^55 - 3278507729301891554176139264 * q^56 + 389758793131386406683302765600 * q^57 - 135342231695310834344564490240 * q^58 - 197343980155337774642230433100 * q^59 + 284004142014605443034712637440 * q^60 - 14811176194679723480587235646 * q^61 - 669787211377795339952819535872 * q^62 + 1932755266001120526055248755036 * q^63 - 396140812571321687967719751680 * q^64 + 617282382727314072782466555610 * q^65 + 3467939277601257961088500105216 * q^66 - 383128478684788296357963882968 * q^67 + 1258203902896699493230105853952 * q^68 - 2467179547237207484008519179080 * q^69 + 5883777307612782450059559567360 * q^70 + 1832518374911281572865798725264 * q^71 + 1481696757199212542013023977472 * q^72 + 11676491506595252901310632876766 * q^73 - 12533948453159681503763339018240 * q^74 + 25446323683166069441840721108800 * q^75 - 28948824511315519663852696371200 * q^76 + 9118295992261211952191322084864 * q^77 + 17794894803607201493766443106304 * q^78 + 21482322024744042017952337060000 * q^79 - 2719667314574969749967176990720 * q^80 + 233126244688526391613091347758507 * q^81 - 21121060322229989613340902162432 * q^82 - 79778192833820459197066044083904 * q^83 + 316052745188365746390700381962240 * q^84 - 273940307850586251212501379351970 * q^85 - 159969464521951510494560167657472 * q^86 + 161485066194342813500375380667040 * q^87 + 48811431496624421114910320099328 * q^88 + 356222635722289986915572638391550 * q^89 + 223166318141007910219452553297920 * q^90 + 412492783458812597073320092809464 * q^91 + 27360272749186754256360802615296 * q^92 - 154490173504452527787707803140688 * q^93 + 187674967622215761178429735567360 * q^94 + 397544657961345230702803428545500 * q^95 - 283273336492734437260186785677312 * q^96 - 752155855759423954859168212154858 * q^97 - 576650432265367709700223374262272 * q^98 - 2786306925474381815060183317128580 * q^99

Decomposition of \(S_{34}^{\mathrm{new}}(\Gamma_1(10))\)

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
10.34.a	\(\chi_{10}(1, \cdot)\)	10.34.a.a	2	1
		10.34.a.b	3
		10.34.a.c	3
		10.34.a.d	3
10.34.b	\(\chi_{10}(9, \cdot)\)	10.34.b.a	16	1

Decomposition of \(S_{34}^{\mathrm{old}}(\Gamma_1(10))\) into lower level spaces

\( S_{34}^{\mathrm{old}}(\Gamma_1(10)) \cong \) \(S_{34}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{34}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{34}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{34}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 1}\)