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

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

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(12))\) 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 3
12.4.a.a 12.a 1.a $1$ $0.708$ \(\Q\) None \(0\) \(3\) \(-18\) \(8\) $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}-18q^{5}+8q^{7}+9q^{9}+6^{2}q^{11}+\cdots\)

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

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