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Properties

Label 12.8
Level 12
Weight 8
Dimension 14
Nonzero newspaces 2
Newform subspaces 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: \( 2 \)
Newform subspaces: \( 4 \)
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

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

Display 100 coefficients 10 coefficients

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 available 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

\( S_{8}^{\mathrm{old}}(\Gamma_1(12)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 1}\)