Space of modular forms of level 3 and weight 38

• Label: 3.38
• Level: 3
• Weight: 38
• Dimension: 7
• Nonzero newspaces: 1
• Newform subspaces: 2
• Sturm bound: 25
• Trace bound: 0

Defining parameters

Level:	\( N \)	=	\( 3 \)
Weight:	\( k \)	=	\( 38 \)
Nonzero newspaces:			\( 1 \)
Newform subspaces:			\( 2 \)
Sturm bound:			\(25\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{38}(\Gamma_1(3))\).

	Total	New	Old
Modular forms	13	7	6
Cusp forms	11	7	4
Eisenstein series	2	0	2

Trace form

7 * q + 126654 * q^2 + 387420489 * q^3 + 684575556340 * q^4 - 13728547643694 * q^5 + 289972613401830 * q^6 + 1983925604451440 * q^7 + 47100204248248488 * q^8 + 1050662447078993847 * q^9 + 10677439113740148564 * q^10 + 43627012209334921596 * q^11 + 2953056363509900916 * q^12 - 116439107414805217342 * q^13 - 1011900338090011919184 * q^14 + 2142004542906729634254 * q^15 + 87255901380513400366096 * q^16 + 53933221344537261354222 * q^17 + 19010085938906126671134 * q^18 + 37431357216330735837572 * q^19 - 7632340044421182766445256 * q^20 + 4349838812892944922819792 * q^21 + 19422800609832966452458824 * q^22 - 23262632371810686242267160 * q^23 + 90605263613645777821825896 * q^24 + 70500389161904121000790441 * q^25 - 190049008972894374663386556 * q^26 + 58149737003040059690390169 * q^27 + 436404251980738279231633760 * q^28 + 4282387159715215775639357514 * q^29 - 4153326304813313427219998844 * q^30 - 2864027368599097964995766872 * q^31 + 9236041216446580613557668000 * q^32 - 666206143987247432978609916 * q^33 + 12435643218207912669769044060 * q^34 + 89869427129508625745958757920 * q^35 + 102751118462092574391065977140 * q^36 + 115863671844314605837317826490 * q^37 - 1107633303229040631381110062344 * q^38 + 85271595592601424874818976542 * q^39 - 930670397641098462628460596752 * q^40 + 1217769522923831842591596907158 * q^41 - 1009658064856086695606942529360 * q^42 + 1974001937268466063840199045564 * q^43 + 7123114228038704575669086836208 * q^44 - 2060581351737727564473739192974 * q^45 - 19159636947469943799013210624752 * q^46 - 7493630272642461617006238652512 * q^47 + 8954664258664264102770633426576 * q^48 + 17777681797108039345187920072047 * q^49 + 6073272961727520596403935775714 * q^50 + 41946140543332132836242206168626 * q^51 + 229991532199618315922613932880152 * q^52 - 241155436559598971130695435510670 * q^53 + 43523333654665393476466329791430 * q^54 - 453860871097216155007773977194104 * q^55 + 679813569394113295052284624175040 * q^56 - 436483358600513385501061741356804 * q^57 - 177250208537205591084553136157468 * q^58 - 231030154028789531327080142644452 * q^59 + 193777584194928096043010367942456 * q^60 - 915631926311408975897805450272158 * q^61 - 3526030476634524366768610629595200 * q^62 + 297776590056517422675871367184240 * q^63 + 7489482758536410774431040832535104 * q^64 - 5918935767911995666073259191789892 * q^65 + 11001043672663058443826467735295592 * q^66 + 20037212315258745158622400365789092 * q^67 - 14964628486001657391340224710150232 * q^68 + 4281679486048626419130782999386776 * q^69 - 34853363080158496834151256770488800 * q^70 - 11256928646966945694391516939711656 * q^71 + 7069487979055025456312146725579048 * q^72 + 13286862853326838922960192885928230 * q^73 - 42636436263036741069505645420848684 * q^74 + 46604114812831642145212466210638599 * q^75 + 251585815873023986043650792581090448 * q^76 - 317311456849407219291248056732618560 * q^77 + 405690213954176805237105803184658548 * q^78 + 117214277910546077013071739760375160 * q^79 - 1573122528355469898112660077331279776 * q^80 + 157698796814574220882881035123408487 * q^81 + 439407919632883552581457950171236460 * q^82 - 780620880363296415782883626608968828 * q^83 + 1744656585209134598679469690579281504 * q^84 + 2058649870565625761770386988960299492 * q^85 - 3018614020714216403538494878879907064 * q^86 + 1572921319640150885314260279379461462 * q^87 + 2856972222974864440117459932508175328 * q^88 - 1919002589120493935902265256833893578 * q^89 + 1602626329682741114871197285917412244 * q^90 + 3074815552050522621982938457870992928 * q^91 - 22025423841918805162477656924353262240 * q^92 + 8079908710240208253230295102126005400 * q^93 + 14581692702710050867156722254196766752 * q^94 - 19671761716261279025385552016851096456 * q^95 + 24717005554576238245245842290026843552 * q^96 + 3135834703288340273897746546516640462 * q^97 - 44762639877851592030494418305208632178 * q^98 + 6548180486657852927733977168615917116 * q^99

Decomposition of \(S_{38}^{\mathrm{new}}(\Gamma_1(3))\)

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
3.38.a	\(\chi_{3}(1, \cdot)\)	3.38.a.a	3	1
		3.38.a.b	4

Decomposition of \(S_{38}^{\mathrm{old}}(\Gamma_1(3))\) into lower level spaces

\( S_{38}^{\mathrm{old}}(\Gamma_1(3)) \cong \) \(S_{38}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 2}\)