Space of modular forms of level 14 and weight 50

• Label: 14.50
• Level: 14
• Weight: 50
• Dimension: 88
• Nonzero newspaces: 2
• Newform subspaces: 6
• Sturm bound: 600
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	=	\( 50 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 6 \)
Sturm bound:			\(600\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{50}(\Gamma_1(14))\).

	Total	New	Old
Modular forms	300	88	212
Cusp forms	288	88	200
Eisenstein series	12	0	12

Trace form

88 * q - 33554432 * q^2 + 35164150554 * q^3 - 2251799813685248 * q^4 + 57294391056677706 * q^5 + 38404500311544692736 * q^6 - 993706997550105940640 * q^7 - 9444732965739290427392 * q^8 - 156500896820248851947508 * q^9 + 2062992256830038454829056 * q^10 - 39618754933709634223223820 * q^11 + 9897828458237151280103424 * q^12 - 4975304738764957413035865538 * q^13 - 6127808908738001960368603136 * q^14 - 486549032692135728182301976728 * q^15 - 633825300114114700748351602688 * q^16 - 2695761325560984258815652013212 * q^17 - 6537232559752655352964992466944 * q^18 + 20475331356473126358656290348142 * q^19 + 111155830386047018921256718172160 * q^20 + 913987284079890463203770107501914 * q^21 - 131824432774046289886148057628672 * q^22 + 4688422851890668289311872812471016 * q^23 + 1187825159289743258639423508578304 * q^24 - 70517163459379495207857969818328188 * q^25 + 43216506731391630943782661108269056 * q^26 - 140139887734218019883039402637977316 * q^27 - 28539131043773348299771871190056960 * q^28 + 57129229652303021959823272284552300 * q^29 + 10094488144792184180848380387690283008 * q^30 + 23369374033205471029664072993857193084 * q^31 - 2658455991569831745807614120560689152 * q^32 - 101752229015511533433210616846476282768 * q^33 - 21202293295216979600529957539228418048 * q^34 - 90766517029776978882058560323266985958 * q^35 + 1948342662874194213023523450376836612096 * q^36 + 759467159092610531913918167460458802764 * q^37 - 954232128789384484493893765264983457792 * q^38 + 4629362693648254143156744974758198843056 * q^39 + 580680697445498735421893429857653620736 * q^40 - 14018549227736264406680085575306707055220 * q^41 + 2492071300249335700438802163133839310848 * q^42 + 62929477888511268252689291028428398360124 * q^43 - 11151688122271106790121057195667667025920 * q^44 - 84243974970137093061277515816178018555998 * q^45 + 51265907533598409850908996744171346722816 * q^46 + 12098967929050844051698073456274924935460 * q^47 + 2785991034768370339692461528031002886144 * q^48 - 378169195352705001584241709299165513193640 * q^49 + 1184576669140541355329371695801223239172096 * q^50 - 1089404917353484089580420890323566153295988 * q^51 + 1073527967770428006131916103204267309924352 * q^52 + 5717655746870498071989077411874019525356672 * q^53 - 15701321756886727172489023207283559141212160 * q^54 + 19625153550115311012745432665364111389448632 * q^55 - 6596691105979764064601797170305412645257216 * q^56 + 76539108797372573275026724936675967526425196 * q^57 - 52979422190154987783604215591167920139403264 * q^58 - 72658393938392624663971916788075789367755170 * q^59 + 2882965615326241394696894349686429611720704 * q^60 + 99726877370403849233370839311561471666493306 * q^61 - 333538335894204766585064556745691994529988608 * q^62 - 393346357090191489658279708947496523769655212 * q^63 + 1962465577470694836455143207993055812526276608 * q^64 + 1882681390774123032486088823831581405311286188 * q^65 - 2100876867339755889909383680233696057152765952 * q^66 - 1480918298563365284710313209514026559771257192 * q^67 - 758789356329765191364380268276095380013187072 * q^68 + 13873581650696266977503255847237357133510752 * q^69 - 1283595490363561548872456670803215880602779648 * q^70 + 8126007194535863601665577728322059764453877304 * q^71 - 1840067382508520773395675825989932879932555264 * q^72 + 11007468720235446748376120061716102625950272328 * q^73 - 4668484801531905940834080933499771221333508096 * q^74 - 8569458180519105236267005040090910327096460050 * q^75 - 22484518386653253811336344737309415690666508288 * q^76 - 47873509404850652261013235741641023586957759372 * q^77 + 29977659633380350568122814952897599569076944896 * q^78 + 4328156255721115898920294240372932776892567032 * q^79 + 4539329325794274537344201098646996891222409216 * q^80 + 223168047739826567408757814565991606711586622292 * q^81 - 8020404897135243524409189724273072730378600448 * q^82 + 564857718965455333892716956537013076527016668230 * q^83 - 225784673745375488881850025582968799914782359552 * q^84 - 128429606072570753430674951830161499636915560588 * q^85 + 322386273128845384963641548837831903320645566464 * q^86 - 897634165789727782794823107453653192393475830988 * q^87 + 433014658825655872016278957714508880724233289728 * q^88 - 3038205764317703497759520251148986440335866229136 * q^89 + 1595712903588590067763815119142222960850504777728 * q^90 - 726720644675154703483224627343499262942820769362 * q^91 + 4784953515990285829424039870481761068586606002176 * q^92 - 6554669575437517985604103700103207971661642512280 * q^93 + 2205965030821735063463772668045058629852473589760 * q^94 + 3395500809884357860577638606708322581148894860296 * q^95 + 334343059047411737171905309942572065432927207424 * q^96 + 15292734813361494627982416396646100990469989347652 * q^97 - 19939650510388948320332968415885817425703911555072 * q^98 + 33217225899110129215500161885016645052246374276996 * q^99

Decomposition of \(S_{50}^{\mathrm{new}}(\Gamma_1(14))\)

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
14.50.a	\(\chi_{14}(1, \cdot)\)	14.50.a.a	5	1
		14.50.a.b	6
		14.50.a.c	6
		14.50.a.d	7
14.50.c	\(\chi_{14}(9, \cdot)\)	14.50.c.a	32	2
		14.50.c.b	32

Decomposition of \(S_{50}^{\mathrm{old}}(\Gamma_1(14))\) into lower level spaces

\( S_{50}^{\mathrm{old}}(\Gamma_1(14)) \cong \) \(S_{50}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{50}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{50}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)