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

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

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

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