↑

Properties

Label 2.18
Level 2
Weight 18
Dimension 1
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 4
Trace bound 0

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 2 \)
Weight: \( k \) = \( 18 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(4\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{18}(\Gamma_1(2))\).

Total New Old
Modular forms 5 1 4
Cusp forms 3 1 2
Eisenstein series 2 0 2

Trace form

\( q + 256 q^{2} + 6084 q^{3} + 65536 q^{4} + 1255110 q^{5} + 1557504 q^{6} - 22465912 q^{7} + 16777216 q^{8} - 92125107 q^{9} + O(q^{10}) \) \( q + 256 q^{2} + 6084 q^{3} + 65536 q^{4} + 1255110 q^{5} + 1557504 q^{6} - 22465912 q^{7} + 16777216 q^{8} - 92125107 q^{9} + 321308160 q^{10} + 172399692 q^{11} + 398721024 q^{12} - 2180149426 q^{13} - 5751273472 q^{14} + 7636089240 q^{15} + 4294967296 q^{16} + 30163933458 q^{17} - 23584027392 q^{18} - 76275766060 q^{19} + 82254888960 q^{20} - 136682608608 q^{21} + 44134321152 q^{22} + 130466597784 q^{23} + 102072582144 q^{24} + 812361658975 q^{25} - 558118253056 q^{26} - 1346177902680 q^{27} - 1472326008832 q^{28} + 803134463070 q^{29} + 1954838845440 q^{30} + 2045336056352 q^{31} + 1099511627776 q^{32} + 1048879726128 q^{33} + 7721966965248 q^{34} - 28197190810320 q^{35} - 6037511012352 q^{36} + 33855367078118 q^{37} - 19526596111360 q^{38} - 13264029107784 q^{39} + 21057251573760 q^{40} + 53206442755242 q^{41} - 34990747803648 q^{42} + 26590357792364 q^{43} + 11298386214912 q^{44} - 115627143046770 q^{45} + 33399449032704 q^{46} - 232565394320592 q^{47} + 26130581028864 q^{48} + 272086688004537 q^{49} + 207964584697600 q^{50} + 183517371158472 q^{51} - 142878272782336 q^{52} - 163277861935626 q^{53} - 344621543086080 q^{54} + 216380577426120 q^{55} - 376915458260992 q^{56} - 464061760709040 q^{57} + 205602422545920 q^{58} + 697820734313340 q^{59} + 500438744432640 q^{60} - 898968337037698 q^{61} + 523606030426112 q^{62} + 2069674546852584 q^{63} + 281474976710656 q^{64} - 2736327346066860 q^{65} + 268513209888768 q^{66} - 2667002109080572 q^{67} + 1976823543103488 q^{68} + 793758780917856 q^{69} - 7218480847441920 q^{70} + 3910637666678472 q^{71} - 1545602819162112 q^{72} + 5855931724867274 q^{73} + 8666973971998208 q^{74} + 4942408333203900 q^{75} - 4998808604508160 q^{76} - 3873116309299104 q^{77} - 3395591451592704 q^{78} - 23821740190145200 q^{79} + 5390656402882560 q^{80} + 3706904974467321 q^{81} + 13620849345341952 q^{82} - 13915745478008556 q^{83} - 8957631437733888 q^{84} + 37859054522470380 q^{85} + 6807131594845184 q^{86} + 4886270073317880 q^{87} + 2892386871017472 q^{88} - 30722744829110310 q^{89} - 29600548619973120 q^{90} + 48979045151366512 q^{91} + 8550258952372224 q^{92} + 12443824566845568 q^{93} - 59536740946071552 q^{94} - 95734476739566600 q^{95} + 6689428743389184 q^{96} + 57649100896826978 q^{97} + 69654192129161472 q^{98} - 15882340072267044 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{18}^{\mathrm{new}}(\Gamma_1(2))\)

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
2.18.a \(\chi_{2}(1, \cdot)\) 2.18.a.a 1 1

Decomposition of \(S_{18}^{\mathrm{old}}(\Gamma_1(2))\) into lower level spaces

\( S_{18}^{\mathrm{old}}(\Gamma_1(2)) \cong \) \(S_{18}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 2}\)