Properties

Label 1.28.a
Level 1
Weight 28
Character orbit a
Rep. character \(\chi_{1}(1,\cdot)\)
Character field \(\Q\)
Dimension 2
Newforms 1
Sturm bound 2
Trace bound 0

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Defining parameters

Level: \( N \) = \( 1 \)
Weight: \( k \) = \( 28 \)
Character orbit: \([\chi]\) = 1.a (trivial)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(2\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{28}(\Gamma_0(1))\).

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

Trace form

\(2q \) \(\mathstrut -\mathstrut 8280q^{2} \) \(\mathstrut -\mathstrut 1286280q^{3} \) \(\mathstrut +\mathstrut 190623296q^{4} \) \(\mathstrut +\mathstrut 5443587900q^{5} \) \(\mathstrut +\mathstrut 86882873184q^{6} \) \(\mathstrut -\mathstrut 175391963600q^{7} \) \(\mathstrut -\mathstrut 3195032348160q^{8} \) \(\mathstrut +\mathstrut 1235136554154q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut -\mathstrut 8280q^{2} \) \(\mathstrut -\mathstrut 1286280q^{3} \) \(\mathstrut +\mathstrut 190623296q^{4} \) \(\mathstrut +\mathstrut 5443587900q^{5} \) \(\mathstrut +\mathstrut 86882873184q^{6} \) \(\mathstrut -\mathstrut 175391963600q^{7} \) \(\mathstrut -\mathstrut 3195032348160q^{8} \) \(\mathstrut +\mathstrut 1235136554154q^{9} \) \(\mathstrut +\mathstrut 39991096148400q^{10} \) \(\mathstrut +\mathstrut 138167337691944q^{11} \) \(\mathstrut -\mathstrut 797895007176960q^{12} \) \(\mathstrut -\mathstrut 753433801271060q^{13} \) \(\mathstrut +\mathstrut 3908340052811712q^{14} \) \(\mathstrut +\mathstrut 8504300488438800q^{15} \) \(\mathstrut -\mathstrut 14322995785166848q^{16} \) \(\mathstrut -\mathstrut 29753620331011740q^{17} \) \(\mathstrut -\mathstrut 110019470226337080q^{18} \) \(\mathstrut +\mathstrut 404565810372684760q^{19} \) \(\mathstrut +\mathstrut 1109219331427200q^{20} \) \(\mathstrut +\mathstrut 723787313583184704q^{21} \) \(\mathstrut -\mathstrut 4583556785578779360q^{22} \) \(\mathstrut +\mathstrut 2929078923121218960q^{23} \) \(\mathstrut +\mathstrut 1677495533792532480q^{24} \) \(\mathstrut +\mathstrut 9119218786673228750q^{25} \) \(\mathstrut -\mathstrut 3003459254146640016q^{26} \) \(\mathstrut -\mathstrut 11127665129740313040q^{27} \) \(\mathstrut -\mathstrut 43065656535315868160q^{28} \) \(\mathstrut -\mathstrut 15546679995448558260q^{29} \) \(\mathstrut +\mathstrut 146561411061600148800q^{30} \) \(\mathstrut +\mathstrut 28544554594467385024q^{31} \) \(\mathstrut +\mathstrut 289738949030869893120q^{32} \) \(\mathstrut -\mathstrut 859077391009750054560q^{33} \) \(\mathstrut -\mathstrut 150938335185934859568q^{34} \) \(\mathstrut -\mathstrut 8958395384765013600q^{35} \) \(\mathstrut +\mathstrut 986344620988374211392q^{36} \) \(\mathstrut +\mathstrut 1867697204682824566780q^{37} \) \(\mathstrut -\mathstrut 485361223888169521440q^{38} \) \(\mathstrut -\mathstrut 690990221801025527472q^{39} \) \(\mathstrut -\mathstrut 8985527186071883904000q^{40} \) \(\mathstrut +\mathstrut 9081343698046512254964q^{41} \) \(\mathstrut -\mathstrut 12195371021026332061440q^{42} \) \(\mathstrut +\mathstrut 5145612605801421773800q^{43} \) \(\mathstrut +\mathstrut 46384541037574305299712q^{44} \) \(\mathstrut -\mathstrut 12080376719602732775700q^{45} \) \(\mathstrut -\mathstrut 51150723570313970279616q^{46} \) \(\mathstrut -\mathstrut 1150251488862201070560q^{47} \) \(\mathstrut -\mathstrut 28878849836569912688640q^{48} \) \(\mathstrut -\mathstrut 92204113217840907690414q^{49} \) \(\mathstrut +\mathstrut 302620649115949014735000q^{50} \) \(\mathstrut -\mathstrut 33494974704727214464656q^{51} \) \(\mathstrut -\mathstrut 21115266673184124022400q^{52} \) \(\mathstrut +\mathstrut 106953735591470060758620q^{53} \) \(\mathstrut -\mathstrut 458020779785618027135040q^{54} \) \(\mathstrut -\mathstrut 214436254091483969701200q^{55} \) \(\mathstrut +\mathstrut 265467760964859260989440q^{56} \) \(\mathstrut -\mathstrut 31800538920577362634080q^{57} \) \(\mathstrut -\mathstrut 74812163717162466470160q^{58} \) \(\mathstrut +\mathstrut 2009620977624026488631880q^{59} \) \(\mathstrut -\mathstrut 694490206253033569881600q^{60} \) \(\mathstrut +\mathstrut 147857426692448940370444q^{61} \) \(\mathstrut -\mathstrut 2352212714010270811080960q^{62} \) \(\mathstrut -\mathstrut 894215232558851858338320q^{63} \) \(\mathstrut -\mathstrut 1234057803938137445761024q^{64} \) \(\mathstrut -\mathstrut 2951949350200452960922200q^{65} \) \(\mathstrut +\mathstrut 11770868153144268253438848q^{66} \) \(\mathstrut +\mathstrut 3051578535738098902157560q^{67} \) \(\mathstrut -\mathstrut 566166870324676171716480q^{68} \) \(\mathstrut -\mathstrut 9376480489705868528695872q^{69} \) \(\mathstrut +\mathstrut 3215012724032159046326400q^{70} \) \(\mathstrut -\mathstrut 13175198820369338598286416q^{71} \) \(\mathstrut -\mathstrut 1487763126543110308830720q^{72} \) \(\mathstrut +\mathstrut 5284260812951286572116660q^{73} \) \(\mathstrut -\mathstrut 24234145145448525537787728q^{74} \) \(\mathstrut +\mathstrut 59486914888952006559645000q^{75} \) \(\mathstrut +\mathstrut 28710432717942786872615680q^{76} \) \(\mathstrut -\mathstrut 42169025756092787413646400q^{77} \) \(\mathstrut -\mathstrut 23925717325436558555851200q^{78} \) \(\mathstrut +\mathstrut 62814351035720719918179040q^{79} \) \(\mathstrut -\mathstrut 68186991639088251432345600q^{80} \) \(\mathstrut -\mathstrut 99047155826597708238103278q^{81} \) \(\mathstrut -\mathstrut 64726649726985190956760560q^{82} \) \(\mathstrut +\mathstrut 171806873410054757883176280q^{83} \) \(\mathstrut +\mathstrut 145152183633423443589998592q^{84} \) \(\mathstrut -\mathstrut 121333441005595565089302600q^{85} \) \(\mathstrut +\mathstrut 252189883901197432712215584q^{86} \) \(\mathstrut -\mathstrut 16722988656204557792643120q^{87} \) \(\mathstrut -\mathstrut 202163623954874235550955520q^{88} \) \(\mathstrut -\mathstrut 313473438761105539763494380q^{89} \) \(\mathstrut -\mathstrut 196904738457998748777517200q^{90} \) \(\mathstrut +\mathstrut 20205365125040878536694304q^{91} \) \(\mathstrut +\mathstrut 602296848225491467788034560q^{92} \) \(\mathstrut -\mathstrut 447293490375807514724002560q^{93} \) \(\mathstrut +\mathstrut 262465434750720041893579392q^{94} \) \(\mathstrut +\mathstrut 1276245244260479145691314000q^{95} \) \(\mathstrut -\mathstrut 562074901098402916384505856q^{96} \) \(\mathstrut -\mathstrut 653202933397052842883888060q^{97} \) \(\mathstrut -\mathstrut 176410316250092689584969240q^{98} \) \(\mathstrut +\mathstrut 1076041779280842335610479688q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{28}^{\mathrm{new}}(\Gamma_0(1))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1.28.a.a \(2\) \(4.619\) \(\Q(\sqrt{18209}) \) None \(-8280\) \(-1286280\) \(5443587900\) \(-175391963600\) \(+\) \(q+(-4140-\beta )q^{2}+(-643140-192\beta )q^{3}+\cdots\)