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Properties

Label 6.30
Level 6
Weight 30
Dimension 5
Nonzero newspaces 1
Newform subspaces 4
Sturm bound 60
Trace bound 0

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Defining parameters

Level: \( N \) = \( 6 = 2 \cdot 3 \)
Weight: \( k \) = \( 30 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 4 \)
Sturm bound: \(60\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{30}(\Gamma_1(6))\).

Total New Old
Modular forms 31 5 26
Cusp forms 27 5 22
Eisenstein series 4 0 4

Trace form

\( 5 q + 16384 q^{2} - 4782969 q^{3} + 1342177280 q^{4} - 39092320506 q^{5} - 78364164096 q^{6} - 1675245256544 q^{7} + 4398046511104 q^{8} + 114383962274805 q^{9} + O(q^{10}) \) \( 5 q + 16384 q^{2} - 4782969 q^{3} + 1342177280 q^{4} - 39092320506 q^{5} - 78364164096 q^{6} - 1675245256544 q^{7} + 4398046511104 q^{8} + 114383962274805 q^{9} - 262657106018304 q^{10} - 299829041328156 q^{11} - 1283918464548864 q^{12} - 10222432593361178 q^{13} + 41611706409156608 q^{14} - 142913126367682686 q^{15} + 360287970189639680 q^{16} + 105549937196566986 q^{17} + 374813367582081024 q^{18} + 8476989425019794908 q^{19} - 10493764881126260736 q^{20} + 17797537741161144384 q^{21} - 41938694461226680320 q^{22} + 37753512611610740280 q^{23} - 21035720123168587776 q^{24} + 302307398505216650411 q^{25} - 501397079436646187008 q^{26} - 109418989131512359209 q^{27} - 449695224352225624064 q^{28} + 1512695815189723307982 q^{29} + 77402910547301400576 q^{30} + 5162499367504416690088 q^{31} + 1180591620717411303424 q^{32} - 7547761413099984474900 q^{33} + 10458588278333911891968 q^{34} + 42472485940960892172864 q^{35} + 30704711072324077486080 q^{36} - 4943519090793952038098 q^{37} + 172403946363652968218624 q^{38} - 47860351961833579916286 q^{39} - 70506480025663778586624 q^{40} - 96617688370948626633534 q^{41} + 123577255326276017455104 q^{42} + 1201303061644999269342436 q^{43} - 80484745430966401499136 q^{44} - 894306902798577981730266 q^{45} - 3751222523690587004731392 q^{46} + 6593969241017804217512640 q^{47} - 344649238497994142121984 q^{48} - 2574562463705742852237699 q^{49} + 11079109234324540832333824 q^{50} - 14192505482713252889469426 q^{51} - 2744063354628170389127168 q^{52} - 4167347374993622439786426 q^{53} - 1792720717930698493280256 q^{54} - 43020524499338257228156680 q^{55} + 11170057384880076643893248 q^{56} - 55778861929669808502177324 q^{57} - 780387229305100239273984 q^{58} + 197638388777049409221696420 q^{59} - 38362950244894525479714816 q^{60} - 243818229456346415181332186 q^{61} + 88014758038558499564552192 q^{62} - 38324238045114984010514784 q^{63} + 96714065569170333976494080 q^{64} + 540895470240622589208114708 q^{65} - 205539171205672188827467776 q^{66} + 70704145370357628340274716 q^{67} + 28333345522131820521455616 q^{68} - 122647783571174717520498072 q^{69} + 568806347411668270856011776 q^{70} - 156786064993066540381141176 q^{71} + 100613197241791537106386944 q^{72} - 643953882755454853073613038 q^{73} + 1531817453034965779414876160 q^{74} + 949384988166166821102287241 q^{75} + 2275524521812366455155458048 q^{76} - 11687604133732350494668976640 q^{77} + 3100208315821389366498459648 q^{78} + 4846947930581774756882152984 q^{79} - 2816898561021913594243055616 q^{80} + 2616738165136802686067557605 q^{81} - 2181215464382351197392175104 q^{82} - 13142495791078179490829323428 q^{83} + 4777490159225801762200879104 q^{84} + 12858635485696755201684600204 q^{85} - 8343580446331549176295260160 q^{86} + 1119450516143847903283705434 q^{87} - 11257832571744058251065425920 q^{88} - 25081707355270373231478737406 q^{89} - 6008752101201428411961606144 q^{90} + 14912069181281021022211467200 q^{91} + 10134381373499479961559367680 q^{92} - 17715884523520482780783360552 q^{93} + 77456292606774227231250579456 q^{94} + 52341213904105303004879629704 q^{95} - 5646733123551136024526585856 q^{96} - 96198608790889440533903935478 q^{97} + 77237571637666616863575392256 q^{98} - 6859126750434149027251181916 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{30}^{\mathrm{new}}(\Gamma_1(6))\)

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
6.30.a \(\chi_{6}(1, \cdot)\) 6.30.a.a 1 1
6.30.a.b 1
6.30.a.c 1
6.30.a.d 2

Decomposition of \(S_{30}^{\mathrm{old}}(\Gamma_1(6))\) into lower level spaces

\( S_{30}^{\mathrm{old}}(\Gamma_1(6)) \cong \) \(S_{30}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{30}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{30}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)