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Properties

Label 2.38
Level 2
Weight 38
Dimension 4
Nonzero newspaces 1
Newform subspaces 2
Sturm bound 9
Trace bound 0

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Defining parameters

Level: \( N \) = \( 2 \)
Weight: \( k \) = \( 38 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 2 \)
Sturm bound: \(9\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{38}(\Gamma_1(2))\).

Total New Old
Modular forms 10 4 6
Cusp forms 8 4 4
Eisenstein series 2 0 2

Trace form

\( 4 q - 78615600 q^{3} + 274877906944 q^{4} - 9324929696040 q^{5} - 242419765346304 q^{6} - 406504794575200 q^{7} + 1870022118371332212 q^{9} + O(q^{10}) \) \( 4 q - 78615600 q^{3} + 274877906944 q^{4} - 9324929696040 q^{5} - 242419765346304 q^{6} - 406504794575200 q^{7} + 1870022118371332212 q^{9} + 4637361809664245760 q^{10} + 29662824384101405808 q^{11} - 5402422895286681600 q^{12} - 568098141485386712200 q^{13} - 1735092632420276502528 q^{14} - 5680830860419105827360 q^{15} + 18889465931478580854784 q^{16} + 166092345674546990416200 q^{17} - 32178957657687510220800 q^{18} - 1187331645010775299663600 q^{19} - 640804289311856331325440 q^{20} + 1037957907379026036306048 q^{21} + 5677270187643854074675200 q^{22} + 28437628681165689800978400 q^{23} - 16658959425061916711583744 q^{24} - 157609474541449481232920900 q^{25} + 70080651700984140986843136 q^{26} - 35249328737993312469727200 q^{27} - 27934796773882915402547200 q^{28} + 1019898325065576960137855160 q^{29} + 3272502404582066951647395840 q^{30} - 5044931989506182998210198912 q^{31} - 39542886088641287642965550400 q^{33} + 43055203916586795813549637632 q^{34} + 27257313622154294863345452480 q^{35} + 128506941459224202151861420032 q^{36} - 244342842739971685438525445800 q^{37} + 476648489279064256600552243200 q^{38} - 1269989421300575130722498191776 q^{39} + 318677076995636996475306639360 q^{40} - 630459916390438110955595460312 q^{41} + 4785834047596026963647948390400 q^{42} - 2142445644790311747845082902800 q^{43} + 2038413770187310084687751282688 q^{44} - 9768698992687879661455893987720 q^{45} + 4845217992050117772649898704896 q^{46} - 9607700580967414160668681819200 q^{47} - 371251674470686880261839257600 q^{48} + 30869913774611510149083682078308 q^{49} - 24091460094454960115060991590400 q^{50} + 67617102766005770789821523069088 q^{51} - 39039407017569868652991427379200 q^{52} + 90754574359927436497098574939800 q^{53} - 420782302071524546329248226344960 q^{54} + 215538537845952176283065263036320 q^{55} - 119234657788410190490160341188608 q^{56} + 369450367774050210270542664532800 q^{57} - 348303278025997360128562141593600 q^{58} + 1331013620448365739742226010780720 q^{59} - 390383724153721606113187552296960 q^{60} - 353989065654942037244215332857032 q^{61} + 1576616316526411494882082711142400 q^{62} - 8305081588797882869072135626668000 q^{63} + 1298074214633706907132624082305024 q^{64} - 339385835151877028329216289910960 q^{65} + 13133254314358366172318608121659392 q^{66} + 3665711708374496818987067079688400 q^{67} + 11413779084609702135244870857523200 q^{68} - 28442084615712409794997576539217536 q^{69} + 1412299692836850246455802074234880 q^{70} - 22391766667452507232398137896774752 q^{71} - 2211321132146185910176027823308800 q^{72} - 4871224337120534176819477926362200 q^{73} - 3248013182587779255808754322505728 q^{74} + 127042227529892469153602963464004400 q^{75} - 81592809357234583674556188826009600 q^{76} + 257576323431634470706604404682275200 q^{77} - 248518528715476089149986488660787200 q^{78} - 126995215811604848308995511956468160 q^{79} - 44035735451695124609492882124963840 q^{80} - 36659914971008034704581161546282396 q^{81} - 416879092969140023747974699312742400 q^{82} + 823463145952413972731717377383018000 q^{83} + 71327924269080222436271756912099328 q^{84} - 178347067147542690901468739681050320 q^{85} + 1111797560771553491927563570539134976 q^{86} - 1454165853712763693375774312151818400 q^{87} + 390139036583778184738021213156147200 q^{88} - 75158905971090583448683889815094040 q^{89} + 2348071989038475617723982685069639680 q^{90} - 6110718130363439317665023326715892032 q^{91} + 1954218962582371981639727628838502400 q^{92} - 5503333341909228136224718980327513600 q^{93} + 3360802553789552011928088899802365952 q^{94} + 13806544056226194570817284809773826400 q^{95} - 1144794974656510320821248717523779584 q^{96} - 613632711409297820260857919695739000 q^{97} + 120119620461738472236394033761484800 q^{98} - 11995052585300668254380468403393277776 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{38}^{\mathrm{new}}(\Gamma_1(2))\)

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
2.38.a \(\chi_{2}(1, \cdot)\) 2.38.a.a 2 1
2.38.a.b 2

Decomposition of \(S_{38}^{\mathrm{old}}(\Gamma_1(2))\) into lower level spaces

\( S_{38}^{\mathrm{old}}(\Gamma_1(2)) \cong \) \(S_{38}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 2}\)