Properties

Label 12.8
Level 12
Weight 8
Dimension 14
Nonzero newspaces 2
Newforms 4
Sturm bound 64
Trace bound 1

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Defining parameters

Level: \( N \) = \( 12 = 2^{2} \cdot 3 \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 2 \)
Newforms: \( 4 \)
Sturm bound: \(64\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(12))\).

Total New Old
Modular forms 33 18 15
Cusp forms 23 14 9
Eisenstein series 10 4 6

Trace form

\(14q \) \(\mathstrut +\mathstrut 24q^{4} \) \(\mathstrut -\mathstrut 108q^{5} \) \(\mathstrut -\mathstrut 216q^{6} \) \(\mathstrut +\mathstrut 280q^{7} \) \(\mathstrut +\mathstrut 2574q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(14q \) \(\mathstrut +\mathstrut 24q^{4} \) \(\mathstrut -\mathstrut 108q^{5} \) \(\mathstrut -\mathstrut 216q^{6} \) \(\mathstrut +\mathstrut 280q^{7} \) \(\mathstrut +\mathstrut 2574q^{9} \) \(\mathstrut -\mathstrut 1200q^{10} \) \(\mathstrut -\mathstrut 8208q^{11} \) \(\mathstrut +\mathstrut 792q^{12} \) \(\mathstrut +\mathstrut 13828q^{13} \) \(\mathstrut +\mathstrut 17496q^{15} \) \(\mathstrut -\mathstrut 14304q^{16} \) \(\mathstrut -\mathstrut 58860q^{17} \) \(\mathstrut -\mathstrut 11376q^{18} \) \(\mathstrut +\mathstrut 35440q^{19} \) \(\mathstrut +\mathstrut 58032q^{21} \) \(\mathstrut +\mathstrut 58224q^{22} \) \(\mathstrut -\mathstrut 92880q^{23} \) \(\mathstrut +\mathstrut 99360q^{24} \) \(\mathstrut +\mathstrut 7274q^{25} \) \(\mathstrut -\mathstrut 169392q^{28} \) \(\mathstrut -\mathstrut 108q^{29} \) \(\mathstrut -\mathstrut 342000q^{30} \) \(\mathstrut -\mathstrut 120392q^{31} \) \(\mathstrut -\mathstrut 150552q^{33} \) \(\mathstrut +\mathstrut 698688q^{34} \) \(\mathstrut +\mathstrut 614736q^{35} \) \(\mathstrut +\mathstrut 950328q^{36} \) \(\mathstrut -\mathstrut 92636q^{37} \) \(\mathstrut -\mathstrut 524880q^{39} \) \(\mathstrut -\mathstrut 1909440q^{40} \) \(\mathstrut +\mathstrut 418500q^{41} \) \(\mathstrut -\mathstrut 2233872q^{42} \) \(\mathstrut -\mathstrut 518960q^{43} \) \(\mathstrut +\mathstrut 125748q^{45} \) \(\mathstrut +\mathstrut 3504480q^{46} \) \(\mathstrut +\mathstrut 1328400q^{47} \) \(\mathstrut +\mathstrut 4119840q^{48} \) \(\mathstrut +\mathstrut 540054q^{49} \) \(\mathstrut -\mathstrut 384912q^{51} \) \(\mathstrut -\mathstrut 5965680q^{52} \) \(\mathstrut -\mathstrut 2043900q^{53} \) \(\mathstrut -\mathstrut 7675560q^{54} \) \(\mathstrut -\mathstrut 606528q^{55} \) \(\mathstrut +\mathstrut 1372464q^{57} \) \(\mathstrut +\mathstrut 10151088q^{58} \) \(\mathstrut -\mathstrut 433728q^{59} \) \(\mathstrut +\mathstrut 12640320q^{60} \) \(\mathstrut +\mathstrut 2129716q^{61} \) \(\mathstrut +\mathstrut 204120q^{63} \) \(\mathstrut -\mathstrut 15471744q^{64} \) \(\mathstrut -\mathstrut 6854760q^{65} \) \(\mathstrut -\mathstrut 16368336q^{66} \) \(\mathstrut -\mathstrut 311360q^{67} \) \(\mathstrut +\mathstrut 4585248q^{69} \) \(\mathstrut +\mathstrut 21838560q^{70} \) \(\mathstrut +\mathstrut 1643760q^{71} \) \(\mathstrut +\mathstrut 22404672q^{72} \) \(\mathstrut +\mathstrut 3111148q^{73} \) \(\mathstrut -\mathstrut 1889568q^{75} \) \(\mathstrut -\mathstrut 27292752q^{76} \) \(\mathstrut -\mathstrut 4298400q^{77} \) \(\mathstrut -\mathstrut 29031696q^{78} \) \(\mathstrut +\mathstrut 1171864q^{79} \) \(\mathstrut -\mathstrut 939762q^{81} \) \(\mathstrut +\mathstrut 30103200q^{82} \) \(\mathstrut +\mathstrut 10620720q^{83} \) \(\mathstrut +\mathstrut 31202640q^{84} \) \(\mathstrut -\mathstrut 4923384q^{85} \) \(\mathstrut -\mathstrut 8485560q^{87} \) \(\mathstrut -\mathstrut 33590592q^{88} \) \(\mathstrut +\mathstrut 3245940q^{89} \) \(\mathstrut -\mathstrut 35812080q^{90} \) \(\mathstrut -\mathstrut 17453680q^{91} \) \(\mathstrut +\mathstrut 6418080q^{93} \) \(\mathstrut +\mathstrut 31652544q^{94} \) \(\mathstrut +\mathstrut 20131200q^{95} \) \(\mathstrut +\mathstrut 34992000q^{96} \) \(\mathstrut +\mathstrut 25180924q^{97} \) \(\mathstrut -\mathstrut 5983632q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(12))\)

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
12.8.a \(\chi_{12}(1, \cdot)\) 12.8.a.a 1 1
12.8.a.b 1
12.8.b \(\chi_{12}(11, \cdot)\) 12.8.b.a 4 1
12.8.b.b 8

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(12))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(12)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)