Space of modular forms of level 36 and weight 18

• Label: 36.18
• Level: 36
• Weight: 18
• Dimension: 275
• Nonzero newspaces: 4
• Sturm bound: 1296
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 36 = 2^{2} \cdot 3^{2} \)
Weight:	\( k \)	=	\( 18 \)
Nonzero newspaces:			\( 4 \)
Sturm bound:			\(1296\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{18}(\Gamma_1(36))\).

	Total	New	Old
Modular forms	632	283	349
Cusp forms	592	275	317
Eisenstein series	40	8	32

Trace form

275 * q - 3 * q^2 + 5880 * q^3 + 109611 * q^4 - 432891 * q^5 + 4960773 * q^6 - 9982943 * q^7 - 106232262 * q^9 - 93416040 * q^10 - 126886539 * q^11 - 262064934 * q^12 - 2728219697 * q^13 + 18019787682 * q^14 - 10344292803 * q^15 + 55858842759 * q^16 + 78733441272 * q^17 - 126269832552 * q^18 + 99600448024 * q^19 + 509168024838 * q^20 + 36717826947 * q^21 + 216377222463 * q^22 - 148125650217 * q^23 + 1601722083531 * q^24 + 5619765368999 * q^25 - 980022146040 * q^27 - 384373228932 * q^28 - 11674819317363 * q^29 + 5751513363918 * q^30 + 1197756010027 * q^31 + 5112694699167 * q^32 - 35265731549865 * q^33 - 17470802012115 * q^34 + 54862599407178 * q^35 + 9171011583 * q^36 - 62116826484110 * q^37 + 68421539093283 * q^38 + 63794709757497 * q^39 - 142447375343118 * q^40 - 140638338411207 * q^41 + 262745330555652 * q^42 - 40146365302511 * q^43 - 492969082498971 * q^45 - 913078501501056 * q^46 + 348645681820269 * q^47 + 896603591205621 * q^48 + 722215046492943 * q^49 - 1376109618108009 * q^50 + 560734535889360 * q^51 - 170198020237668 * q^52 - 364884829437252 * q^53 + 735131978267187 * q^54 - 108482721336342 * q^55 - 4671948171553470 * q^56 + 1735783480361496 * q^57 + 4270188029786802 * q^58 - 1985499588604029 * q^59 - 5195589075436590 * q^60 + 7671822596539015 * q^61 + 1733422822356777 * q^63 + 10360605154032522 * q^64 - 18741475593737685 * q^65 - 21697392711794718 * q^66 + 14124928188227071 * q^67 + 32045449764096165 * q^68 - 6617351767213845 * q^69 - 7879301573325252 * q^70 - 17550389884123464 * q^71 - 15419950330033341 * q^72 + 23605848830200102 * q^73 + 63388177380697434 * q^74 + 3726408171941820 * q^75 - 10522459613819823 * q^76 - 72418629294800397 * q^77 - 40163361565645932 * q^78 + 33594673653798421 * q^79 + 22131500405116146 * q^81 + 51512427159066054 * q^82 - 106077196657288071 * q^83 - 71744010268751346 * q^84 - 27156337005982530 * q^85 - 6553889578079835 * q^86 + 43533512846525691 * q^87 + 12804417425881299 * q^88 - 205525115454667884 * q^89 - 31246088812628562 * q^90 + 221258427854155178 * q^91 - 40969825008929796 * q^92 + 22213568810678295 * q^93 - 307318912958501304 * q^94 - 211342993451526228 * q^95 + 719760354178792428 * q^96 - 195999986588452457 * q^97 - 69762554894010591 * q^99

Decomposition of \(S_{18}^{\mathrm{new}}(\Gamma_1(36))\)

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
36.18.a	\(\chi_{36}(1, \cdot)\)	36.18.a.a	1	1
		36.18.a.b	1
		36.18.a.c	1
		36.18.a.d	2
		36.18.a.e	2
36.18.b	\(\chi_{36}(35, \cdot)\)	36.18.b.a	2	1
		36.18.b.b	32
36.18.e	\(\chi_{36}(13, \cdot)\)	36.18.e.a	34	2
36.18.h	\(\chi_{36}(11, \cdot)\)	n/a	200	2

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{18}^{\mathrm{old}}(\Gamma_1(36))\) into lower level spaces

\( S_{18}^{\mathrm{old}}(\Gamma_1(36)) \cong \) \(S_{18}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 9}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 3}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 2}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)