Properties

Label 1.12
Level 1
Weight 12
Dimension 1
Nonzero newspaces 1
Newforms 1
Sturm bound 1
Trace bound 0

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Defining parameters

Level: \( N \) = \( 1 \)
Weight: \( k \) = \( 12 \)
Nonzero newspaces: \( 1 \)
Newforms: \( 1 \)
Sturm bound: \(1\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_1(1))\).

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

Trace form

\(q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut +\mathstrut 252q^{3} \) \(\mathstrut -\mathstrut 1472q^{4} \) \(\mathstrut +\mathstrut 4830q^{5} \) \(\mathstrut -\mathstrut 6048q^{6} \) \(\mathstrut -\mathstrut 16744q^{7} \) \(\mathstrut +\mathstrut 84480q^{8} \) \(\mathstrut -\mathstrut 113643q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut +\mathstrut 252q^{3} \) \(\mathstrut -\mathstrut 1472q^{4} \) \(\mathstrut +\mathstrut 4830q^{5} \) \(\mathstrut -\mathstrut 6048q^{6} \) \(\mathstrut -\mathstrut 16744q^{7} \) \(\mathstrut +\mathstrut 84480q^{8} \) \(\mathstrut -\mathstrut 113643q^{9} \) \(\mathstrut -\mathstrut 115920q^{10} \) \(\mathstrut +\mathstrut 534612q^{11} \) \(\mathstrut -\mathstrut 370944q^{12} \) \(\mathstrut -\mathstrut 577738q^{13} \) \(\mathstrut +\mathstrut 401856q^{14} \) \(\mathstrut +\mathstrut 1217160q^{15} \) \(\mathstrut +\mathstrut 987136q^{16} \) \(\mathstrut -\mathstrut 6905934q^{17} \) \(\mathstrut +\mathstrut 2727432q^{18} \) \(\mathstrut +\mathstrut 10661420q^{19} \) \(\mathstrut -\mathstrut 7109760q^{20} \) \(\mathstrut -\mathstrut 4219488q^{21} \) \(\mathstrut -\mathstrut 12830688q^{22} \) \(\mathstrut +\mathstrut 18643272q^{23} \) \(\mathstrut +\mathstrut 21288960q^{24} \) \(\mathstrut -\mathstrut 25499225q^{25} \) \(\mathstrut +\mathstrut 13865712q^{26} \) \(\mathstrut -\mathstrut 73279080q^{27} \) \(\mathstrut +\mathstrut 24647168q^{28} \) \(\mathstrut +\mathstrut 128406630q^{29} \) \(\mathstrut -\mathstrut 29211840q^{30} \) \(\mathstrut -\mathstrut 52843168q^{31} \) \(\mathstrut -\mathstrut 196706304q^{32} \) \(\mathstrut +\mathstrut 134722224q^{33} \) \(\mathstrut +\mathstrut 165742416q^{34} \) \(\mathstrut -\mathstrut 80873520q^{35} \) \(\mathstrut +\mathstrut 167282496q^{36} \) \(\mathstrut -\mathstrut 182213314q^{37} \) \(\mathstrut -\mathstrut 255874080q^{38} \) \(\mathstrut -\mathstrut 145589976q^{39} \) \(\mathstrut +\mathstrut 408038400q^{40} \) \(\mathstrut +\mathstrut 308120442q^{41} \) \(\mathstrut +\mathstrut 101267712q^{42} \) \(\mathstrut -\mathstrut 17125708q^{43} \) \(\mathstrut -\mathstrut 786948864q^{44} \) \(\mathstrut -\mathstrut 548895690q^{45} \) \(\mathstrut -\mathstrut 447438528q^{46} \) \(\mathstrut +\mathstrut 2687348496q^{47} \) \(\mathstrut +\mathstrut 248758272q^{48} \) \(\mathstrut -\mathstrut 1696965207q^{49} \) \(\mathstrut +\mathstrut 611981400q^{50} \) \(\mathstrut -\mathstrut 1740295368q^{51} \) \(\mathstrut +\mathstrut 850430336q^{52} \) \(\mathstrut -\mathstrut 1596055698q^{53} \) \(\mathstrut +\mathstrut 1758697920q^{54} \) \(\mathstrut +\mathstrut 2582175960q^{55} \) \(\mathstrut -\mathstrut 1414533120q^{56} \) \(\mathstrut +\mathstrut 2686677840q^{57} \) \(\mathstrut -\mathstrut 3081759120q^{58} \) \(\mathstrut -\mathstrut 5189203740q^{59} \) \(\mathstrut -\mathstrut 1791659520q^{60} \) \(\mathstrut +\mathstrut 6956478662q^{61} \) \(\mathstrut +\mathstrut 1268236032q^{62} \) \(\mathstrut +\mathstrut 1902838392q^{63} \) \(\mathstrut +\mathstrut 2699296768q^{64} \) \(\mathstrut -\mathstrut 2790474540q^{65} \) \(\mathstrut -\mathstrut 3233333376q^{66} \) \(\mathstrut -\mathstrut 15481826884q^{67} \) \(\mathstrut +\mathstrut 10165534848q^{68} \) \(\mathstrut +\mathstrut 4698104544q^{69} \) \(\mathstrut +\mathstrut 1940964480q^{70} \) \(\mathstrut +\mathstrut 9791485272q^{71} \) \(\mathstrut -\mathstrut 9600560640q^{72} \) \(\mathstrut +\mathstrut 1463791322q^{73} \) \(\mathstrut +\mathstrut 4373119536q^{74} \) \(\mathstrut -\mathstrut 6425804700q^{75} \) \(\mathstrut -\mathstrut 15693610240q^{76} \) \(\mathstrut -\mathstrut 8951543328q^{77} \) \(\mathstrut +\mathstrut 3494159424q^{78} \) \(\mathstrut +\mathstrut 38116845680q^{79} \) \(\mathstrut +\mathstrut 4767866880q^{80} \) \(\mathstrut +\mathstrut 1665188361q^{81} \) \(\mathstrut -\mathstrut 7394890608q^{82} \) \(\mathstrut -\mathstrut 29335099668q^{83} \) \(\mathstrut +\mathstrut 6211086336q^{84} \) \(\mathstrut -\mathstrut 33355661220q^{85} \) \(\mathstrut +\mathstrut 411016992q^{86} \) \(\mathstrut +\mathstrut 32358470760q^{87} \) \(\mathstrut +\mathstrut 45164021760q^{88} \) \(\mathstrut -\mathstrut 24992917110q^{89} \) \(\mathstrut +\mathstrut 13173496560q^{90} \) \(\mathstrut +\mathstrut 9673645072q^{91} \) \(\mathstrut -\mathstrut 27442896384q^{92} \) \(\mathstrut -\mathstrut 13316478336q^{93} \) \(\mathstrut -\mathstrut 64496363904q^{94} \) \(\mathstrut +\mathstrut 51494658600q^{95} \) \(\mathstrut -\mathstrut 49569988608q^{96} \) \(\mathstrut +\mathstrut 75013568546q^{97} \) \(\mathstrut +\mathstrut 40727164968q^{98} \) \(\mathstrut -\mathstrut 60754911516q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(1))\)

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
1.12.a \(\chi_{1}(1, \cdot)\) 1.12.a.a 1 1