Space of modular forms of level 7 and weight 39

• Label: 7.39
• Level: 7
• Weight: 39
• Dimension: 73
• Nonzero newspaces: 2
• Newform subspaces: 3
• Sturm bound: 156
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 7 \)
Weight:	\( k \)	=	\( 39 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 3 \)
Sturm bound:			\(156\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{39}(\Gamma_1(7))\).

	Total	New	Old
Modular forms	79	79	0
Cusp forms	73	73	0
Eisenstein series	6	6	0

Trace form

73 * q - 3 * q^2 + 1162261464 * q^3 + 549755813885 * q^4 + 19815543546960 * q^5 - 14188855519736359 * q^7 - 414001115611363719 * q^8 + 76999642091187321 * q^9 - 21221680220863104780 * q^10 - 164964396438449840070 * q^11 - 1621301977610523942132 * q^12 + 6530897522625963794433 * q^14 + 78965862463375075674720 * q^15 - 29119110517753609209959 * q^16 + 406984398652544708781408 * q^17 + 3644683332713385547062465 * q^18 - 167572074305232723252672 * q^19 + 39477299272145327085346056 * q^21 + 63508790460314074337307162 * q^22 - 54608199007875452702669238 * q^23 - 254997777331818910279461816 * q^24 + 304196889911806561875723025 * q^25 + 1253822859857086607484441864 * q^26 - 8837031279657375019637831195 * q^28 - 12458548340440413903785374086 * q^29 + 98001510355348777467002326320 * q^30 - 129813354378524697893229986496 * q^31 + 107453828764047494914810241865 * q^32 - 439148747291288968888224022872 * q^33 + 739102301387103022560504636960 * q^35 - 5918963602328947093423929857751 * q^36 + 964748097899048841352658545138 * q^37 + 1660991630986240884736219249680 * q^38 + 581200093017312839799025448424 * q^39 + 10192275175089433552610088790080 * q^40 - 17430719031972839532656965241448 * q^42 + 32099175160218399522640045832122 * q^43 - 165329331439416477875934341777298 * q^44 + 238345580948571076922104324041720 * q^45 - 141310112597353250489336351207742 * q^46 + 22752568545774663573723690238224 * q^47 + 9572551342546733714471352443977 * q^49 + 579579292552446811710449737376625 * q^50 - 243379924203643516954823875492608 * q^51 + 270070091154696708770976277042392 * q^52 - 7706620091074914530630605227150 * q^53 + 4791283368082714655147622422783232 * q^54 - 1253999781566996493259478497658703 * q^56 + 13437110201444628632761308557733072 * q^57 - 30835321718309849959691196122164422 * q^58 + 29338192934208325475890830033830184 * q^59 - 71560221664961301259395952845973980 * q^60 + 10956195835774718788899029465566344 * q^61 - 80506456949315276968104604398753327 * q^63 + 244302703325074973607351846903478673 * q^64 - 94205140401743392628508816908808360 * q^65 + 126189778421182064281098295971215484 * q^66 + 41108053016410744850701617674795426 * q^67 - 218287858729543604979750265961739348 * q^68 + 470587937021111276593667191110638880 * q^70 - 571486482371470863812360113147419774 * q^71 + 1560416496468644759212764157622504769 * q^72 - 1760534728843754322874504945891620648 * q^73 + 3937886871435688800140966781171036726 * q^74 - 1369647790314715668718998864559782960 * q^75 + 1561416416408583230272704731879638458 * q^77 - 4263561695986325337022120302613558272 * q^78 + 6977259724297989581987527303306383578 * q^79 - 7710455555764402322475509750570679720 * q^80 - 6337800346692540034722415087397334375 * q^81 + 5562421542454337773414461141725491992 * q^82 - 4392118988968130045273317057048348548 * q^84 + 9462558238530860868459043750420774320 * q^85 - 6267013355246173593970757648810289318 * q^86 - 972544381506009723245535843857085672 * q^87 + 12683694488461118236583469915501289266 * q^88 + 9164899727479461651558176395344597960 * q^89 - 4050410851707101387399873669270175504 * q^91 + 33064004559325012779922783298932194906 * q^92 + 22889429846340264509240472712309856424 * q^93 + 47246297874414014315113884937785740112 * q^94 - 265151363017223663120308843207597376760 * q^95 + 330435500265862959142478545594692726960 * q^96 - 624791619572648021065139043972530699931 * q^98 + 310743717648903227399358158518415174010 * q^99

Decomposition of \(S_{39}^{\mathrm{new}}(\Gamma_1(7))\)

We only show spaces with odd 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
7.39.b	\(\chi_{7}(6, \cdot)\)	7.39.b.a	1	1
		7.39.b.b	24
7.39.d	\(\chi_{7}(3, \cdot)\)	7.39.d.a	48	2