Properties

Label 12.8.a
Level 12
Weight 8
Character orbit a
Rep. character \(\chi_{12}(1,\cdot)\)
Character field \(\Q\)
Dimension 2
Newforms 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: \(\Q\)
Newforms: \( 2 \)
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

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

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

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

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