Space of modular forms of level 23 and weight 29

• Label: 23.29
• Level: 23
• Weight: 29
• Dimension: 605
• Nonzero newspaces: 2
• Newform subspaces: 3
• Sturm bound: 1276
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 23 \)
Weight:	\( k \)	=	\( 29 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 3 \)
Sturm bound:			\(1276\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{29}(\Gamma_1(23))\).

	Total	New	Old
Modular forms	627	627	0
Cusp forms	605	605	0
Eisenstein series	22	22	0

Trace form

605 * 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 - 34127469042724068 * q^15 + 589083034389577717 * q^16 + 323147318868110374 * q^17 - 4072522733895024651 * q^18 + 859499544664592392 * q^19 - 515752782754480139 * q^20 - 1888517680426461524 * q^21 + 11516436813803028019 * q^23 - 145662011795709100054 * q^24 + 133887297597405615175 * q^25 - 289942033128616230923 * q^26 + 789956633964916706134 * q^27 - 1692320459909643632651 * q^28 + 655320335049003476842 * q^29 - 4522236522272066633739 * q^30 + 2383894277032729956748 * q^31 - 8569023691601939005451 * q^32 - 11335735698620710883946 * q^33 - 1697894796717859309009 * q^34 - 2371222465283203125011 * q^35 + 83672070978017046179644 * q^36 - 81947617325026649035851 * q^37 + 132164791617128012532394 * q^38 - 150427082778886448233787 * q^39 + 377156232305810546874989 * q^40 - 69374548040280534871259 * q^41 - 235572692133669446580761 * q^42 + 456861872872107442046373 * q^43 - 1016746899243094265328918 * q^44 + 2174211352932379713920957 * q^46 - 1361415963041716972206982 * q^47 - 770182874344683305574739 * q^48 + 4374646043393430937971685 * q^49 - 4541940987110137939453136 * q^50 - 2265973227311990368200347 * q^51 + 18414906336562835284827939 * q^52 - 2733245891335785977799659 * q^53 + 1772050217193280799996925 * q^54 + 32051975354148923972768783 * q^55 - 64074930040693561001667248 * q^56 + 38790850977721152193406050 * q^57 - 58654442215591448150728386 * q^58 + 69727546335852918964688017 * q^59 - 127258217687120940075986341 * q^60 - 26760444681917154820809439 * q^61 + 112285803854898617610534901 * q^62 - 49564276916114289532092186 * q^63 - 156387038630027204302471179 * q^64 + 201833358841854205909775398 * q^65 + 100242641821189480170092304 * q^66 - 97934312456021729060459097 * q^67 + 365345736074247580673859684 * q^69 - 151934542971621390503378966 * q^70 - 524396801792701279972064546 * q^71 + 596138946644772705366739162 * q^72 + 294395534294520853808827059 * q^73 - 1977778254662856233123195132 * q^74 - 3738679025677708297465104308 * q^75 + 3485311200679672785570095958 * q^76 - 312046535640018039104551604 * q^77 + 2677272670456266751548094899 * q^78 - 2729838243383464067467643767 * q^79 + 9047563669113223183034777518 * q^80 + 4420051064083845412412097281 * q^81 - 6574954426090708545791302465 * q^82 + 3737797913048509379174028880 * q^83 + 3093551076793531843094804891 * q^84 + 4399655710891303692080435283 * q^85 - 20656295060810455028927572925 * q^86 + 4748638133678656376622050005 * q^87 + 15503302378038601753162610877 * q^88 - 2301751906697467239472748819 * q^89 - 50244316573561215969652942846 * q^90 + 31967103543495398346262932826 * q^92 + 11499423012690898084038487226 * q^93 - 40631778648395986622602658704 * q^94 - 20666398627114675919873807264 * q^95 + 41174001813563557277878836616 * q^96 + 64987956999165160443575724412 * q^97 - 99070266196836150071307528659 * q^98 - 35907152496147942293023520792 * q^99

Decomposition of \(S_{29}^{\mathrm{new}}(\Gamma_1(23))\)

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
23.29.b	\(\chi_{23}(22, \cdot)\)	23.29.b.a	3	1
		23.29.b.b	52
23.29.d	\(\chi_{23}(5, \cdot)\)	23.29.d.a	550	10