Properties

Label 4.12.a
Level 4
Weight 12
Character orbit a
Rep. character \(\chi_{4}(1,\cdot)\)
Character field \(\Q\)
Dimension 1
Newforms 1
Sturm bound 6
Trace bound 0

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Defining parameters

Level: \( N \) = \( 4 = 2^{2} \)
Weight: \( k \) = \( 12 \)
Character orbit: \([\chi]\) = 4.a (trivial)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(6\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_0(4))\).

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

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)Dim.
\(-\)\(1\)

Trace form

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

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_0(4))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2
4.12.a.a \(1\) \(3.073\) \(\Q\) None \(0\) \(-516\) \(-10530\) \(49304\) \(-\) \(q-516q^{3}-10530q^{5}+49304q^{7}+\cdots\)

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_0(4))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_0(4)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 3}\)