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Properties

Label 4.12.a
Level $4$
Weight $12$
Character orbit 4.a
Rep. character $\chi_{4}(1,\cdot)$
Character field $\Q$
Dimension $1$
Newform subspaces $1$
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: \(\Q\)
Newform subspaces: \( 1 \)
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

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_0(4))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2
4.12.a.a 4.a 1.a $1$ $3.073$ \(\Q\) None \(0\) \(-516\) \(-10530\) \(49304\) $-$ $\mathrm{SU}(2)$ \(q-516q^{3}-10530q^{5}+49304q^{7}+\cdots\)

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

\( S_{12}^{\mathrm{old}}(\Gamma_0(4)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 2}\)