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Properties

Label 6012.2.a
Level $6012$
Weight $2$
Character orbit 6012.a
Rep. character $\chi_{6012}(1,\cdot)$
Character field $\Q$
Dimension $68$
Newform subspaces $11$
Sturm bound $2016$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 6012 = 2^{2} \cdot 3^{2} \cdot 167 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6012.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 11 \)
Sturm bound: \(2016\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6012))\).

Total New Old
Modular forms 1020 68 952
Cusp forms 997 68 929
Eisenstein series 23 0 23

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(3\)\(167\)FrickeDim
\(-\)\(+\)\(+\)$-$\(13\)
\(-\)\(+\)\(-\)$+$\(13\)
\(-\)\(-\)\(+\)$+$\(21\)
\(-\)\(-\)\(-\)$-$\(21\)
Plus space\(+\)\(34\)
Minus space\(-\)\(34\)

Trace form

\( 68 q - 2 q^{5} + 8 q^{7} + O(q^{10}) \) \( 68 q - 2 q^{5} + 8 q^{7} + 6 q^{11} + 2 q^{17} - 10 q^{19} - 2 q^{23} + 80 q^{25} - 2 q^{29} + 2 q^{31} + 2 q^{35} + 18 q^{37} - 4 q^{43} - 2 q^{47} + 68 q^{49} - 8 q^{53} - 2 q^{55} + 18 q^{59} - 6 q^{61} - 14 q^{65} + 20 q^{67} + 4 q^{71} + 14 q^{73} - 16 q^{77} - 22 q^{79} - 14 q^{83} - 18 q^{85} - 6 q^{89} + 30 q^{91} - 8 q^{95} - 24 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6012))\) 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 3 167
6012.2.a.a 6012.a 1.a $2$ $48.006$ \(\Q(\sqrt{13}) \) None \(0\) \(0\) \(6\) \(3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{5}+(2-\beta )q^{7}+(5-\beta )q^{13}-\beta q^{17}+\cdots\)
6012.2.a.b 6012.a 1.a $3$ $48.006$ 3.3.148.1 None \(0\) \(0\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{5}+2\beta _{2}q^{7}+(-1-\beta _{1}-\beta _{2})q^{11}+\cdots\)
6012.2.a.c 6012.a 1.a $3$ $48.006$ 3.3.148.1 None \(0\) \(0\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{5}+2\beta _{2}q^{7}+(1+\beta _{1}+\beta _{2})q^{11}+\cdots\)
6012.2.a.d 6012.a 1.a $5$ $48.006$ 5.5.826865.1 None \(0\) \(0\) \(-10\) \(9\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}+(2-\beta _{3})q^{7}+(-\beta _{1}-\beta _{2}-\beta _{3}+\cdots)q^{11}+\cdots\)
6012.2.a.e 6012.a 1.a $5$ $48.006$ 5.5.149169.1 None \(0\) \(0\) \(3\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(\beta _{1}-\beta _{3}+\beta _{4})q^{5}+(-\beta _{1}-\beta _{4})q^{7}+\cdots\)
6012.2.a.f 6012.a 1.a $5$ $48.006$ 5.5.161121.1 None \(0\) \(0\) \(7\) \(-2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{3}+\beta _{4})q^{5}+(-1+\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots\)
6012.2.a.g 6012.a 1.a $7$ $48.006$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(0\) \(2\) \(-12\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-\beta _{1}+\beta _{2}-\beta _{3})q^{5}+(-2-\beta _{1}+\cdots)q^{7}+\cdots\)
6012.2.a.h 6012.a 1.a $9$ $48.006$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(0\) \(-9\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{5}-\beta _{6}q^{7}+(-1+\beta _{5}+\cdots)q^{11}+\cdots\)
6012.2.a.i 6012.a 1.a $9$ $48.006$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(0\) \(-1\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{5}+(-\beta _{3}-\beta _{6})q^{7}+(1+\beta _{7}+\cdots)q^{11}+\cdots\)
6012.2.a.j 6012.a 1.a $10$ $48.006$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(0\) \(-6\) \(4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{3})q^{5}+\beta _{1}q^{7}+(-\beta _{2}+\beta _{3}+\cdots)q^{11}+\cdots\)
6012.2.a.k 6012.a 1.a $10$ $48.006$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(0\) \(6\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{3})q^{5}+\beta _{1}q^{7}+(\beta _{2}-\beta _{3}-\beta _{6}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6012))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6012)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(167))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(334))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(501))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(668))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1002))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1503))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2004))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3006))\)\(^{\oplus 2}\)