Properties

Label 1.18
Level 1
Weight 18
Dimension 1
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 1
Trace bound 0

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Defining parameters

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

Dimensions

The following table gives the dimensions of various subspaces of \(M_{18}(\Gamma_1(1))\).

Total New Old
Modular forms 2 2 0
Cusp forms 1 1 0
Eisenstein series 1 1 0

Trace form

\( q - 528 q^{2} - 4284 q^{3} + 147712 q^{4} - 1025850 q^{5} + 2261952 q^{6} + 3225992 q^{7} - 8785920 q^{8} - 110787507 q^{9} + O(q^{10}) \) \( q - 528 q^{2} - 4284 q^{3} + 147712 q^{4} - 1025850 q^{5} + 2261952 q^{6} + 3225992 q^{7} - 8785920 q^{8} - 110787507 q^{9} + 541648800 q^{10} - 753618228 q^{11} - 632798208 q^{12} + 2541064526 q^{13} - 1703323776 q^{14} + 4394741400 q^{15} - 14721941504 q^{16} - 5429742318 q^{17} + 58495803696 q^{18} + 1487499860 q^{19} - 151530355200 q^{20} - 13820149728 q^{21} + 397910424384 q^{22} - 317091823464 q^{23} + 37638881280 q^{24} + 289428769375 q^{25} - 1341682069728 q^{26} + 1027850138280 q^{27} + 476517730304 q^{28} + 2433410602590 q^{29} - 2320423459200 q^{30} - 8849722053088 q^{31} + 8924773220352 q^{32} + 3228500488752 q^{33} + 2866903943904 q^{34} - 3309383893200 q^{35} - 16364644233984 q^{36} + 12691652946662 q^{37} - 785399926080 q^{38} - 10885920429384 q^{39} + 9013036032000 q^{40} + 48864151002282 q^{41} + 7297039056384 q^{42} - 91019974317844 q^{43} - 111318455694336 q^{44} + 113651364055950 q^{45} + 167424482788992 q^{46} - 49304994276048 q^{47} + 63068797403136 q^{48} - 222223489603143 q^{49} - 152818390230000 q^{50} + 23261016090312 q^{51} + 375345723264512 q^{52} + 22940453195766 q^{53} - 542704873011840 q^{54} + 773099259193800 q^{55} - 28343307632640 q^{56} - 6372449400240 q^{57} - 1284840798167520 q^{58} + 32695090729980 q^{59} + 649156041676800 q^{60} - 1308285854869378 q^{61} + 4672653244030464 q^{62} - 357399611281944 q^{63} - 2782645943533568 q^{64} - 2606751043997100 q^{65} - 1704648258061056 q^{66} + 5196143861984132 q^{67} - 802038097276416 q^{68} + 1358421371719776 q^{69} + 1747354695609600 q^{70} - 3709489877412408 q^{71} + 973370173501440 q^{72} + 3402372968272586 q^{73} - 6701192755837536 q^{74} - 1239912848002500 q^{75} + 219721579320320 q^{76} - 2431166374582176 q^{77} + 5747765986714752 q^{78} + 2366533941308240 q^{79} + 15102503691878400 q^{80} + 9903806719952121 q^{81} - 25800271729204896 q^{82} - 29766750443172204 q^{83} - 2041401956622336 q^{84} + 5570101156920300 q^{85} + 48058546439821632 q^{86} - 10424731021495560 q^{87} + 6621229461749760 q^{88} + 29167184100574170 q^{89} - 60007920221541600 q^{90} + 8197453832359792 q^{91} - 46838267427514368 q^{92} + 37912209275428992 q^{93} + 26033036977753344 q^{94} - 1525951731381000 q^{95} - 38233728475987968 q^{96} - 63769879140957598 q^{97} + 117334002510459504 q^{98} + 83491484709877596 q^{99} + O(q^{100}) \)

Decomposition of \(S_{18}^{\mathrm{new}}(\Gamma_1(1))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
1.18.a \(\chi_{1}(1, \cdot)\) 1.18.a.a 1 1