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Properties

Label 3012.2.a
Level $3012$
Weight $2$
Character orbit 3012.a
Rep. character $\chi_{3012}(1,\cdot)$
Character field $\Q$
Dimension $42$
Newform subspaces $9$
Sturm bound $1008$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 3012 = 2^{2} \cdot 3 \cdot 251 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3012.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 9 \)
Sturm bound: \(1008\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3012))\).

Total New Old
Modular forms 510 42 468
Cusp forms 499 42 457
Eisenstein series 11 0 11

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

\(2\)\(3\)\(251\)FrickeDim
\(-\)\(+\)\(+\)$-$\(12\)
\(-\)\(+\)\(-\)$+$\(9\)
\(-\)\(-\)\(+\)$+$\(9\)
\(-\)\(-\)\(-\)$-$\(12\)
Plus space\(+\)\(18\)
Minus space\(-\)\(24\)

Trace form

\( 42 q + 4 q^{5} + 42 q^{9} + O(q^{10}) \) \( 42 q + 4 q^{5} + 42 q^{9} + 4 q^{13} - 4 q^{15} + 8 q^{17} - 12 q^{19} - 4 q^{23} + 42 q^{25} - 8 q^{31} - 8 q^{33} - 16 q^{35} - 8 q^{39} + 4 q^{41} - 20 q^{43} + 4 q^{45} + 4 q^{47} + 34 q^{49} - 8 q^{51} + 8 q^{53} - 24 q^{55} - 4 q^{57} - 16 q^{59} - 4 q^{61} + 4 q^{65} + 20 q^{67} - 8 q^{69} + 8 q^{71} + 4 q^{73} + 8 q^{75} + 32 q^{77} - 16 q^{79} + 42 q^{81} - 8 q^{83} + 20 q^{85} - 12 q^{87} + 36 q^{89} + 16 q^{95} - 12 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3012))\) 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 3 251
3012.2.a.a 3012.a 1.a $1$ $24.051$ \(\Q\) None \(0\) \(1\) \(-3\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-3q^{5}+q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots\)
3012.2.a.b 3012.a 1.a $1$ $24.051$ \(\Q\) None \(0\) \(1\) \(-2\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}+2q^{7}+q^{9}+6q^{11}+\cdots\)
3012.2.a.c 3012.a 1.a $1$ $24.051$ \(\Q\) None \(0\) \(1\) \(-1\) \(5\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+5q^{7}+q^{9}-6q^{11}-2q^{13}+\cdots\)
3012.2.a.d 3012.a 1.a $1$ $24.051$ \(\Q\) None \(0\) \(1\) \(2\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{5}+2q^{7}+q^{9}-2q^{11}+\cdots\)
3012.2.a.e 3012.a 1.a $1$ $24.051$ \(\Q\) None \(0\) \(1\) \(3\) \(-3\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+3q^{5}-3q^{7}+q^{9}-6q^{13}+\cdots\)
3012.2.a.f 3012.a 1.a $6$ $24.051$ 6.6.4443861.1 None \(0\) \(6\) \(-4\) \(-3\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+(-\beta _{1}-\beta _{2}+\beta _{3})q^{5}+(-1+\cdots)q^{7}+\cdots\)
3012.2.a.g 3012.a 1.a $9$ $24.051$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(-9\) \(-3\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+\beta _{5}q^{5}-\beta _{7}q^{7}+q^{9}+(1+\beta _{1}+\cdots)q^{11}+\cdots\)
3012.2.a.h 3012.a 1.a $10$ $24.051$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(10\) \(5\) \(-4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+(1-\beta _{1})q^{5}+\beta _{3}q^{7}+q^{9}-\beta _{2}q^{11}+\cdots\)
3012.2.a.i 3012.a 1.a $12$ $24.051$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-12\) \(7\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(1-\beta _{1})q^{5}+\beta _{6}q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3012))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(3012)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(251))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(502))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(753))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1004))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1506))\)\(^{\oplus 2}\)