Properties

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

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 4 = 2^{2} \)
Weight: \( k \) = \( 12 \)
Nonzero newspaces: \( 1 \)
Newforms: \( 1 \)
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

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

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

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