Properties

Label 12.8.a
Level $12$
Weight $8$
Character orbit 12.a
Rep. character $\chi_{12}(1,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $2$
Sturm bound $16$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 12 = 2^{2} \cdot 3 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 12.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(16\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(12))\).

Total New Old
Modular forms 17 2 15
Cusp forms 11 2 9
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
\(-\)\(+\)$-$\(1\)
\(-\)\(-\)$+$\(1\)
Plus space\(+\)\(1\)
Minus space\(-\)\(1\)

Trace form

\( 2 q - 108 q^{5} + 280 q^{7} + 1458 q^{9} + O(q^{10}) \) \( 2 q - 108 q^{5} + 280 q^{7} + 1458 q^{9} - 8208 q^{11} + 10300 q^{13} + 17496 q^{15} - 58860 q^{17} + 35440 q^{19} + 52488 q^{21} - 92880 q^{23} + 59534 q^{25} - 108 q^{29} - 120392 q^{31} - 87480 q^{33} + 614736 q^{35} - 244100 q^{37} - 524880 q^{39} + 418500 q^{41} - 518960 q^{43} - 78732 q^{45} + 1328400 q^{47} + 281682 q^{49} - 384912 q^{51} - 2043900 q^{53} - 606528 q^{55} + 1837080 q^{57} - 433728 q^{59} + 3900844 q^{61} + 204120 q^{63} - 6854760 q^{65} - 311360 q^{67} + 3709152 q^{69} + 1643760 q^{71} + 465460 q^{73} - 1889568 q^{75} - 4298400 q^{77} + 1171864 q^{79} + 1062882 q^{81} + 10620720 q^{83} - 1440504 q^{85} - 8485560 q^{87} + 3245940 q^{89} - 17453680 q^{91} - 2361960 q^{93} + 20131200 q^{95} + 12096100 q^{97} - 5983632 q^{99} + O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(12))\) 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
12.8.a.a 12.a 1.a $1$ $3.749$ \(\Q\) None \(0\) \(-27\) \(-378\) \(-832\) $-$ $+$ $\mathrm{SU}(2)$ \(q-3^{3}q^{3}-378q^{5}-832q^{7}+3^{6}q^{9}+\cdots\)
12.8.a.b 12.a 1.a $1$ $3.749$ \(\Q\) None \(0\) \(27\) \(270\) \(1112\) $-$ $-$ $\mathrm{SU}(2)$ \(q+3^{3}q^{3}+270q^{5}+1112q^{7}+3^{6}q^{9}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_0(12))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_0(12)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 2}\)