↑

Properties

Label 18.34
Level 18
Weight 34
Dimension 80
Nonzero newspaces 2
Newform subspaces 10
Sturm bound 612
Trace bound 1

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 18 = 2 \cdot 3^{2} \)
Weight: \( k \) = \( 34 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 10 \)
Sturm bound: \(612\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{34}(\Gamma_1(18))\).

Total New Old
Modular forms 305 80 225
Cusp forms 289 80 209
Eisenstein series 16 0 16

Trace form

\( 80 q - 65536 q^{2} + 81602355 q^{3} - 81604378624 q^{4} - 343058410602 q^{5} - 1684700725248 q^{6} + 49630166404612 q^{7} + 562949953421312 q^{8} + 4946293753929021 q^{9} + O(q^{10}) \) \( 80 q - 65536 q^{2} + 81602355 q^{3} - 81604378624 q^{4} - 343058410602 q^{5} - 1684700725248 q^{6} + 49630166404612 q^{7} + 562949953421312 q^{8} + 4946293753929021 q^{9} + 14602515202965504 q^{10} - 325981936243093785 q^{11} + 424729891427057664 q^{12} - 364113641952170444 q^{13} - 12035028765710090240 q^{14} + 38751611264562114234 q^{15} - 350488137400481480704 q^{16} - 794939673451005284874 q^{17} - 226504084431154053120 q^{18} + 3613745998682659080754 q^{19} - 1473424654153329672192 q^{20} + 30753809774826214338828 q^{21} - 10518015947537670537216 q^{22} + 75340930411059443326824 q^{23} - 27673305503525435867136 q^{24} - 909201075487643263510711 q^{25} + 798699797276756640268288 q^{26} - 1751784086132745535606896 q^{27} + 1085245587012148013301760 q^{28} - 6249503939722580569181676 q^{29} + 1583583746645237340045312 q^{30} - 3623863894284811916392814 q^{31} - 1208925819614629174706176 q^{32} - 18269120245443973081337529 q^{33} + 16581505220912637920083968 q^{34} - 71138366674373695345190892 q^{35} + 22388774482149067198562304 q^{36} + 78707606973423900489503476 q^{37} - 103192229901646140939370496 q^{38} + 220716561411684991658011314 q^{39} + 62717325236079641896157184 q^{40} - 2038717507532902055686557045 q^{41} + 2068211687923487824693690368 q^{42} - 1939328175481355954822848607 q^{43} + 1095777573400234498845573120 q^{44} - 16446028594872148359890876226 q^{45} + 2856733194770558100675231744 q^{46} - 3072122862494958353681072364 q^{47} - 3329498751809836434245812224 q^{48} - 31748657361136688400853503981 q^{49} - 20116934319512702942384422912 q^{50} - 96709611042813375218026413225 q^{51} - 1563856184212025653197799424 q^{52} - 305479852054731611255502937632 q^{53} + 218170499735655844595532103680 q^{54} + 130871439659832018311146265172 q^{55} - 51690054955144083798008791040 q^{56} - 231560028953333061974961620511 q^{57} + 73314349294363221358320156672 q^{58} - 73182256534084819820320202871 q^{59} - 162742486685557164267395874816 q^{60} + 721665796457919011856180778690 q^{61} + 731628648658530547131085225984 q^{62} - 1739556206110535771588888679906 q^{63} + 6338253001141147007483516026880 q^{64} - 4748126942137436668874818939374 q^{65} - 109614193851667834869664186368 q^{66} + 5754986775196462001766765495427 q^{67} - 2208350539825141775554937094144 q^{68} + 7472352233684080554862180980114 q^{69} + 2776131897190111443237853986816 q^{70} - 22047498695588609706536918804856 q^{71} - 2648783811001107952958850465792 q^{72} + 23480191297090106856328989276142 q^{73} - 13385006039449554486481989140480 q^{74} - 10706559320588612661199358964153 q^{75} + 8055623408041021221140193869824 q^{76} - 56701199410190941691279242353252 q^{77} + 5880237642835853107673658163200 q^{78} + 45472416061248044318277447179110 q^{79} - 4169915622098096549500758786048 q^{80} - 71602969308738673471167909935511 q^{81} - 71808494082455796919388563439616 q^{82} + 66976062359151388577716690494 q^{83} - 24331937823833266427160938151936 q^{84} - 27054365497516122702708351682620 q^{85} - 383035062773555903453284546838528 q^{86} - 179366772962689644576002904703836 q^{87} - 45174534513480746685365470887936 q^{88} - 458664377047525246129565889771492 q^{89} + 442310704319505658954307636035584 q^{90} - 451877721725155685793434065508404 q^{91} + 323586832165712145800674519547904 q^{92} + 344374700417527499679222266705778 q^{93} - 202154012751840831241478259474432 q^{94} + 2204937660380588975280674147674968 q^{95} + 149933185229301287330674611585024 q^{96} - 3603988766331412130093976631414325 q^{97} + 8229163512105388514423656584708096 q^{98} - 3342475716939197113955604616673424 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{34}^{\mathrm{new}}(\Gamma_1(18))\)

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
18.34.a \(\chi_{18}(1, \cdot)\) 18.34.a.a 1 1
18.34.a.b 1
18.34.a.c 1
18.34.a.d 1
18.34.a.e 2
18.34.a.f 2
18.34.a.g 3
18.34.a.h 3
18.34.c \(\chi_{18}(7, \cdot)\) 18.34.c.a 32 2
18.34.c.b 34

Decomposition of \(S_{34}^{\mathrm{old}}(\Gamma_1(18))\) into lower level spaces

\( S_{34}^{\mathrm{old}}(\Gamma_1(18)) \cong \) \(S_{34}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{34}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{34}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{34}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{34}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)