Properties

Label 4.12
Level 4
Weight 12
Dimension 1
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 12
Trace bound 0

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Defining parameters

Level: \( N \) = \( 4 = 2^{2} \)
Weight: \( k \) = \( 12 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(12\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_1(4))\).

Total New Old
Modular forms 7 1 6
Cusp forms 4 1 3
Eisenstein series 3 0 3

Trace form

\( q - 516 q^{3} - 10530 q^{5} + 49304 q^{7} + 89109 q^{9} + O(q^{10}) \) \( q - 516 q^{3} - 10530 q^{5} + 49304 q^{7} + 89109 q^{9} - 309420 q^{11} - 1723594 q^{13} + 5433480 q^{15} - 2279502 q^{17} + 4550444 q^{19} - 25440864 q^{21} - 7282872 q^{23} + 62052775 q^{25} + 45427608 q^{27} - 69040026 q^{29} - 141740704 q^{31} + 159660720 q^{33} - 519171120 q^{35} + 711366974 q^{37} + 889374504 q^{39} - 1225262214 q^{41} - 33606220 q^{43} - 938317770 q^{45} + 123214608 q^{47} + 453557673 q^{49} + 1176223032 q^{51} + 1106121582 q^{53} + 3258192600 q^{55} - 2348029104 q^{57} - 9062779932 q^{59} - 3854150458 q^{61} + 4393430136 q^{63} + 18149444820 q^{65} - 15313764676 q^{67} + 3757961952 q^{69} + 20619626328 q^{71} - 2063718694 q^{73} - 32019231900 q^{75} - 15255643680 q^{77} + 13689871472 q^{79} - 39226037751 q^{81} + 65570428908 q^{83} + 24003156060 q^{85} + 35624653416 q^{87} - 29715508854 q^{89} - 84980078576 q^{91} + 73138203264 q^{93} - 47916175320 q^{95} - 23439626206 q^{97} - 27572106780 q^{99} + O(q^{100}) \)

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(4))\)

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
4.12.a \(\chi_{4}(1, \cdot)\) 4.12.a.a 1 1

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_1(4))\) into lower level spaces

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