Space of modular forms of level 7 and weight 50

• Label: 7.50
• Level: 7
• Weight: 50
• Dimension: 89
• Nonzero newspaces: 2
• Newform subspaces: 3
• Sturm bound: 200
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 7 \)
Weight:	\( k \)	=	\( 50 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 3 \)
Sturm bound:			\(200\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{50}(\Gamma_1(7))\).

	Total	New	Old
Modular forms	101	93	8
Cusp forms	95	89	6
Eisenstein series	6	4	2

Trace form

89 * q + 48450333 * q^2 + 371479848324 * q^3 - 1188905442812419 * q^4 - 137776781743200426 * q^5 - 46242560528423238534 * q^6 + 775278329555655267041 * q^7 - 9068047443949002891105 * q^8 - 769127517445175223072219 * q^9 + 1484852002754291115254622 * q^10 + 113551102176449721038204268 * q^11 - 941743309139455177542198102 * q^12 - 37184094235077620173737506 * q^13 - 26923411216979731629877325127 * q^14 + 335099576712031387992019860312 * q^15 + 99640084805116267600827793457 * q^16 + 1698492923013727186358585897538 * q^17 + 8957767203057714622648354624659 * q^18 - 16652160172459329934283894963084 * q^19 - 825405673550925056554798720741344 * q^20 - 154096002020144352793568046133212 * q^21 - 2223414116134607616961808343056364 * q^22 - 670871700244086673665771037533576 * q^23 + 32483717265492644671858757310540786 * q^24 + 64639128879918812683372013417897351 * q^25 - 40273306775559633698235540851499372 * q^26 + 226192481235483599518238584974907560 * q^27 + 727589808262903977769384224338849477 * q^28 - 544854463541258243031364048625143698 * q^29 - 22521776976556576759945227875918532186 * q^30 - 12781357972857853197803681958566496992 * q^31 + 21734092336913795160148624869187815903 * q^32 + 33260888181161285326301032518446399568 * q^33 - 233716772553834109221230664864925417698 * q^34 - 16202928086297554863122153709356058042 * q^35 + 2734477161016771904724895543448599869897 * q^36 + 162757898883173245447301456778314798998 * q^37 - 1635593299773130646193568960567815714840 * q^38 - 4924497373428813391381389370012592431848 * q^39 + 5229041926306749844998478751854374854880 * q^40 + 7486139565383735425060454143679797488090 * q^41 + 30038357707914941193665269066988204881542 * q^42 - 48332490371970251115962982666206233179956 * q^43 + 88307045722644474616130728357225254551172 * q^44 + 113588470799033575102402727293508698090110 * q^45 - 190778735914791835916184155340178247652546 * q^46 + 22852584364690981972758659945421234562608 * q^47 - 1870540916641359317732850339011539018409346 * q^48 + 2272280237253786442416279467423784227486681 * q^49 - 28300570877197966550546763295953510419907 * q^50 - 49659255395146542864271290891008294743800 * q^51 - 1958091212626952743471402163061075631784612 * q^52 - 144384254412614618082552068877819283404186 * q^53 + 20438717020195324292274463656698104015734690 * q^54 - 18224420890949670758687347312449610818932088 * q^55 + 14841158999949492028497753209592578204091855 * q^56 - 59369826862414526165469138520508958769878000 * q^57 + 77487410582248602527191961336237448108651570 * q^58 + 143300713885734087714212991388962534633511740 * q^59 - 162076082746510882060210162680108787836449076 * q^60 - 62833405500642397354370896529192518484136914 * q^61 + 161623382050869677303086402103759766505757736 * q^62 - 32020308934909530559944597003823960608695187 * q^63 + 1403337508331152450794696986129407379936543489 * q^64 + 185156728449716786821794212392063073385351444 * q^65 - 1761780994418978537060024241722273089563978186 * q^66 + 4364303082815955957291338726897595126032297668 * q^67 - 6997959115787960656754489870445819904621761774 * q^68 + 6297146796475687131650458791598377340531049760 * q^69 - 4940165621360474666955048813952249785224679174 * q^70 + 4246701518737502936206513081713819488962601928 * q^71 - 12604346165614929446249719007946220228135722945 * q^72 - 10255849708866910948410641016314308384431514406 * q^73 - 23576702177743554738781512593010233114373915312 * q^74 + 56810250015746036160669157811386055402013773148 * q^75 - 52621391322600950574093239455314205434814263086 * q^76 + 67455628621488469996168405752122096482420800972 * q^77 - 109030583282518753863396941652351440290415563872 * q^78 + 12393317073343899499456816819336151929850051440 * q^79 + 145915136767023053963425972908425409770903347728 * q^80 - 235396038821936771619053078483879456650527233007 * q^81 + 483736226428545340341910755088437026391539180046 * q^82 - 1012865805513135835002064562629007399538411657996 * q^83 + 1897796332647065831696503262304985235020105477746 * q^84 - 1070561359073558394118020656190300034542554978100 * q^85 + 449096828099015693228954871651422565410579214600 * q^86 + 115649722702293579719315882478444931888680059160 * q^87 - 2168577164750611566389103872532113845496478730560 * q^88 + 2053279863976225507387546124489044830323718988458 * q^89 - 2034392927886469743364381198565975866214114099364 * q^90 + 703493196098303081248825965360742274573834328526 * q^91 - 9998092346166760202574658081208838847842239525592 * q^92 - 910638930350107775845079686817341823977393395552 * q^93 + 8634347551763583556292883061976275328333783765394 * q^94 - 1626944151251296008849735994139577019009798655208 * q^95 + 43080657298357286553494412932290678742156981842914 * q^96 - 9479340836098262920131390304550918629793117062382 * q^97 + 59141084900532280512210410353608617105018083496013 * q^98 - 30394711522732087915558458888910548398085364451076 * q^99

Decomposition of \(S_{50}^{\mathrm{new}}(\Gamma_1(7))\)

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
7.50.a	\(\chi_{7}(1, \cdot)\)	7.50.a.a	12	1
		7.50.a.b	13
7.50.c	\(\chi_{7}(2, \cdot)\)	7.50.c.a	64	2

Decomposition of \(S_{50}^{\mathrm{old}}(\Gamma_1(7))\) into lower level spaces

\( S_{50}^{\mathrm{old}}(\Gamma_1(7)) \cong \) \(S_{50}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 2}\)