Properties

Label 6012.2.a
Level 6012
Weight 2
Character orbit a
Rep. character \(\chi_{6012}(1,\cdot)\)
Character field \(\Q\)
Dimension 68
Newforms 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: \(\Q\)
Newforms: \( 11 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6012))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 167
6012.2.a.a \(2\) \(48.006\) \(\Q(\sqrt{13}) \) None \(0\) \(0\) \(6\) \(3\) \(-\) \(-\) \(-\) \(q+3q^{5}+(2-\beta )q^{7}+(5-\beta )q^{13}-\beta q^{17}+\cdots\)
6012.2.a.b \(3\) \(48.006\) 3.3.148.1 None \(0\) \(0\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q-\beta _{2}q^{5}+2\beta _{2}q^{7}+(-1-\beta _{1}-\beta _{2})q^{11}+\cdots\)
6012.2.a.c \(3\) \(48.006\) 3.3.148.1 None \(0\) \(0\) \(0\) \(0\) \(-\) \(+\) \(+\) \(q+\beta _{2}q^{5}+2\beta _{2}q^{7}+(1+\beta _{1}+\beta _{2})q^{11}+\cdots\)
6012.2.a.d \(5\) \(48.006\) 5.5.826865.1 None \(0\) \(0\) \(-10\) \(9\) \(-\) \(-\) \(-\) \(q-2q^{5}+(2-\beta _{3})q^{7}+(-\beta _{1}-\beta _{2}-\beta _{3}+\cdots)q^{11}+\cdots\)
6012.2.a.e \(5\) \(48.006\) 5.5.149169.1 None \(0\) \(0\) \(3\) \(-2\) \(-\) \(-\) \(+\) \(q+(\beta _{1}-\beta _{3}+\beta _{4})q^{5}+(-\beta _{1}-\beta _{4})q^{7}+\cdots\)
6012.2.a.f \(5\) \(48.006\) 5.5.161121.1 None \(0\) \(0\) \(7\) \(-2\) \(-\) \(-\) \(-\) \(q+(1+\beta _{3}+\beta _{4})q^{5}+(-1+\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots\)
6012.2.a.g \(7\) \(48.006\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(0\) \(2\) \(-12\) \(-\) \(-\) \(+\) \(q+(-\beta _{1}+\beta _{2}-\beta _{3})q^{5}+(-2-\beta _{1}+\cdots)q^{7}+\cdots\)
6012.2.a.h \(9\) \(48.006\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(0\) \(-9\) \(2\) \(-\) \(-\) \(+\) \(q+(-1+\beta _{1})q^{5}-\beta _{6}q^{7}+(-1+\beta _{5}+\cdots)q^{11}+\cdots\)
6012.2.a.i \(9\) \(48.006\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(0\) \(-1\) \(2\) \(-\) \(-\) \(-\) \(q-\beta _{1}q^{5}+(-\beta _{3}-\beta _{6})q^{7}+(1+\beta _{7}+\cdots)q^{11}+\cdots\)
6012.2.a.j \(10\) \(48.006\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(0\) \(-6\) \(4\) \(-\) \(+\) \(-\) \(q+(-1-\beta _{3})q^{5}+\beta _{1}q^{7}+(-\beta _{2}+\beta _{3}+\cdots)q^{11}+\cdots\)
6012.2.a.k \(10\) \(48.006\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(0\) \(6\) \(4\) \(-\) \(+\) \(+\) \(q+(1+\beta _{3})q^{5}+\beta _{1}q^{7}+(\beta _{2}-\beta _{3}-\beta _{6}+\cdots)q^{11}+\cdots\)

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

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