Properties

Label 12.4.a
Level $12$
Weight $4$
Character orbit 12.a
Rep. character $\chi_{12}(1,\cdot)$
Character field $\Q$
Dimension $1$
Newform subspaces $1$
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: \(\Q\)
Newform subspaces: \( 1 \)
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

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

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

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

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