Properties

Label 12.4.a
Level 12
Weight 4
Character orbit a
Rep. character \(\chi_{12}(1,\cdot)\)
Character field \(\Q\)
Dimension 1
Newforms 1
Sturm bound 8
Trace bound 0

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Defining parameters

Level: \( N \) = \( 12 = 2^{2} \cdot 3 \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 12.a (trivial)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(8\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 9 1 8
Cusp forms 3 1 2
Eisenstein series 6 0 6

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

\(2\)\(3\)FrickeDim.
\(-\)\(-\)\(+\)\(1\)
Plus space\(+\)\(1\)
Minus space\(-\)\(0\)

Trace form

\(q \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut 18q^{5} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 9q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut 18q^{5} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 9q^{9} \) \(\mathstrut +\mathstrut 36q^{11} \) \(\mathstrut -\mathstrut 10q^{13} \) \(\mathstrut -\mathstrut 54q^{15} \) \(\mathstrut +\mathstrut 18q^{17} \) \(\mathstrut -\mathstrut 100q^{19} \) \(\mathstrut +\mathstrut 24q^{21} \) \(\mathstrut +\mathstrut 72q^{23} \) \(\mathstrut +\mathstrut 199q^{25} \) \(\mathstrut +\mathstrut 27q^{27} \) \(\mathstrut -\mathstrut 234q^{29} \) \(\mathstrut -\mathstrut 16q^{31} \) \(\mathstrut +\mathstrut 108q^{33} \) \(\mathstrut -\mathstrut 144q^{35} \) \(\mathstrut -\mathstrut 226q^{37} \) \(\mathstrut -\mathstrut 30q^{39} \) \(\mathstrut +\mathstrut 90q^{41} \) \(\mathstrut +\mathstrut 452q^{43} \) \(\mathstrut -\mathstrut 162q^{45} \) \(\mathstrut +\mathstrut 432q^{47} \) \(\mathstrut -\mathstrut 279q^{49} \) \(\mathstrut +\mathstrut 54q^{51} \) \(\mathstrut +\mathstrut 414q^{53} \) \(\mathstrut -\mathstrut 648q^{55} \) \(\mathstrut -\mathstrut 300q^{57} \) \(\mathstrut -\mathstrut 684q^{59} \) \(\mathstrut +\mathstrut 422q^{61} \) \(\mathstrut +\mathstrut 72q^{63} \) \(\mathstrut +\mathstrut 180q^{65} \) \(\mathstrut +\mathstrut 332q^{67} \) \(\mathstrut +\mathstrut 216q^{69} \) \(\mathstrut -\mathstrut 360q^{71} \) \(\mathstrut +\mathstrut 26q^{73} \) \(\mathstrut +\mathstrut 597q^{75} \) \(\mathstrut +\mathstrut 288q^{77} \) \(\mathstrut +\mathstrut 512q^{79} \) \(\mathstrut +\mathstrut 81q^{81} \) \(\mathstrut -\mathstrut 1188q^{83} \) \(\mathstrut -\mathstrut 324q^{85} \) \(\mathstrut -\mathstrut 702q^{87} \) \(\mathstrut -\mathstrut 630q^{89} \) \(\mathstrut -\mathstrut 80q^{91} \) \(\mathstrut -\mathstrut 48q^{93} \) \(\mathstrut +\mathstrut 1800q^{95} \) \(\mathstrut -\mathstrut 1054q^{97} \) \(\mathstrut +\mathstrut 324q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3
12.4.a.a \(1\) \(0.708\) \(\Q\) None \(0\) \(3\) \(-18\) \(8\) \(-\) \(-\) \(q+3q^{3}-18q^{5}+8q^{7}+9q^{9}+6^{2}q^{11}+\cdots\)

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

\( S_{4}^{\mathrm{old}}(\Gamma_0(12)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 2}\)