Space of modular forms of level 23 and weight 31

• Label: 23.31
• Level: 23
• Weight: 31
• Dimension: 649
• Nonzero newspaces: 2
• Newform subspaces: 4
• Sturm bound: 1364
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 23 \)
Weight:	\( k \)	=	\( 31 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 4 \)
Sturm bound:			\(1364\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{31}(\Gamma_1(23))\).

	Total	New	Old
Modular forms	671	671	0
Cusp forms	649	649	0
Eisenstein series	22	22	0

Trace form

649 * q - 11 * q^2 - 11 * q^3 - 11 * q^4 - 11 * q^5 - 11 * q^6 - 11 * q^7 - 11 * q^8 - 11 * q^9 - 11 * q^10 - 11 * q^11 - 11 * q^12 - 11 * q^13 - 11 * q^14 + 1888459891557523581 * q^15 + 2916509380352409589 * q^16 + 6141760561475910789 * q^17 + 65954701312060030965 * q^18 - 36626049237336688811 * q^19 + 153392625590529425397 * q^20 - 67988527827441731411 * q^21 - 10062944948858758363 * q^23 + 804951017948341862378 * q^24 - 1203633116603054381387 * q^25 + 3595511311319626547189 * q^26 - 12949494517233482300411 * q^27 + 35662723755297227145205 * q^28 - 16082571446126961483411 * q^29 + 91062982067521035173877 * q^30 - 3183044296527880983011 * q^31 - 280970628939402916659211 * q^32 - 237277788254386285012827 * q^33 - 711619762870908244781681 * q^34 - 943175995009155273437511 * q^35 + 932072938242028262175364 * q^36 + 1428378497900819782983061 * q^37 - 3617801833687586618948886 * q^38 + 3687768017373889749171949 * q^39 - 5957870168741455078125011 * q^40 - 590141217348708622663011 * q^41 + 25797531026218879749894919 * q^42 - 21416374393968676119855011 * q^43 + 40180884460531598750409058 * q^44 - 90982816645799417393676611 * q^46 + 74268461748212250676570050 * q^47 - 56132217870731647098185875 * q^48 - 148251161717805841583331971 * q^49 + 351029448211193084716796864 * q^50 - 118717088916880904292156611 * q^51 - 463609608274004112575301581 * q^52 + 260611453253782029709943589 * q^53 - 1027237204371954132111495171 * q^54 + 676448748769109400234846685 * q^55 + 1527302114039519250092727144 * q^56 - 2216153710596500029006582139 * q^57 + 3679416986248239515743808014 * q^58 - 597503195205096514583961591 * q^59 - 9358529172054253189504869781 * q^60 + 3723303325675088901886213909 * q^61 - 5190879012312157104365568011 * q^62 - 1333681847062858320496711011 * q^63 + 13540911612309357531632762869 * q^64 - 9416014920744143710326484475 * q^65 - 11397420755047451682980548632 * q^66 + 6399352552588353846862571989 * q^67 - 24674352238355035415585564211 * q^69 + 21998348675389581216398966762 * q^70 + 30854441198001257180225501389 * q^71 - 87503470225557869163374129150 * q^72 - 11844282545228742064047873611 * q^73 + 23064324112283654108935114044 * q^74 - 113150713372138400761225690091 * q^75 - 249937659186303259354652498546 * q^76 + 151320355163920448768284272789 * q^77 + 16772290959969974773537607139 * q^78 - 215276382827313017964798894971 * q^79 + 460341399684191274245185573318 * q^80 - 452147212615310124267146328691 * q^81 - 337632308630625749057308798961 * q^82 + 550605915117053147008455933189 * q^83 - 1400507069158520854121147121301 * q^84 - 226458329711397720833214597455 * q^85 + 337048954956812743638921219699 * q^86 + 356116806823636769305335586789 * q^87 - 1388970815891469206414850079875 * q^88 - 54357497501614699345697069711 * q^89 + 4541926083717923921152321341482 * q^90 - 2958973955852359010421060079886 * q^92 - 116456704676556247252701507022 * q^93 + 4079963731342148373414241265000 * q^94 + 1439870139531376874044014669741 * q^95 - 14137712632871027231839316874992 * q^96 - 1361322970673145949919060930495 * q^97 + 7189250272609137391604107804653 * q^98 + 5269803331430526955464508479589 * q^99

Decomposition of \(S_{31}^{\mathrm{new}}(\Gamma_1(23))\)

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
23.31.b	\(\chi_{23}(22, \cdot)\)	23.31.b.a	1	1
		23.31.b.b	2
		23.31.b.c	56
23.31.d	\(\chi_{23}(5, \cdot)\)	23.31.d.a	590	10