Properties

Label 12.12.a
Level $12$
Weight $12$
Character orbit 12.a
Rep. character $\chi_{12}(1,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $2$
Sturm bound $24$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 12 = 2^{2} \cdot 3 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 12.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(24\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 25 2 23
Cusp forms 19 2 17
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

\( 2 q + 12852 q^{5} - 77000 q^{7} + 118098 q^{9} + O(q^{10}) \) \( 2 q + 12852 q^{5} - 77000 q^{7} + 118098 q^{9} - 137808 q^{11} + 1092700 q^{13} - 1732104 q^{15} - 2702700 q^{17} + 170800 q^{19} + 23147208 q^{21} - 25261200 q^{23} + 10334894 q^{25} - 226450188 q^{29} + 374152408 q^{31} + 358230600 q^{33} - 834294384 q^{35} - 135236900 q^{37} + 732207600 q^{39} - 1031482620 q^{41} + 1563677200 q^{43} + 758897748 q^{45} - 4139780400 q^{47} + 3546699282 q^{49} + 1436386608 q^{51} - 2251057500 q^{53} - 6139603008 q^{55} - 153527400 q^{57} + 14284492992 q^{59} - 700025396 q^{61} - 4546773000 q^{63} - 3717354600 q^{65} - 1966587200 q^{67} - 14765714208 q^{69} + 25293783600 q^{71} - 13777935500 q^{73} - 22261000608 q^{75} + 75518805600 q^{77} - 35976619976 q^{79} + 6973568802 q^{81} - 3501565200 q^{83} - 38434553784 q^{85} - 13860768600 q^{87} - 55164907980 q^{89} + 101443739600 q^{91} + 22426810200 q^{93} + 3349296000 q^{95} + 93399168100 q^{97} - 8137424592 q^{99} + O(q^{100}) \)

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_0(12))\) 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
12.12.a.a 12.a 1.a $1$ $9.220$ \(\Q\) None \(0\) \(-243\) \(9990\) \(-86128\) $-$ $+$ $\mathrm{SU}(2)$ \(q-3^{5}q^{3}+9990q^{5}-86128q^{7}+3^{10}q^{9}+\cdots\)
12.12.a.b 12.a 1.a $1$ $9.220$ \(\Q\) None \(0\) \(243\) \(2862\) \(9128\) $-$ $-$ $\mathrm{SU}(2)$ \(q+3^{5}q^{3}+2862q^{5}+9128q^{7}+3^{10}q^{9}+\cdots\)

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

\( S_{12}^{\mathrm{old}}(\Gamma_0(12)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 2}\)