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Properties

Label 6036.2.a
Level $6036$
Weight $2$
Character orbit 6036.a
Rep. character $\chi_{6036}(1,\cdot)$
Character field $\Q$
Dimension $84$
Newform subspaces $9$
Sturm bound $2016$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 6036 = 2^{2} \cdot 3 \cdot 503 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6036.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 9 \)
Sturm bound: \(2016\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6036))\).

Total New Old
Modular forms 1014 84 930
Cusp forms 1003 84 919
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.

\(2\)\(3\)\(503\)FrickeDim
\(-\)\(+\)\(+\)$-$\(26\)
\(-\)\(+\)\(-\)$+$\(16\)
\(-\)\(-\)\(+\)$+$\(16\)
\(-\)\(-\)\(-\)$-$\(26\)
Plus space\(+\)\(32\)
Minus space\(-\)\(52\)

Trace form

\( 84 q + 4 q^{5} + 4 q^{7} + 84 q^{9} + O(q^{10}) \) \( 84 q + 4 q^{5} + 4 q^{7} + 84 q^{9} - 4 q^{11} + 4 q^{13} + 4 q^{15} + 4 q^{17} - 8 q^{19} - 8 q^{23} + 92 q^{25} + 8 q^{29} + 4 q^{31} + 8 q^{33} - 8 q^{35} + 12 q^{37} - 8 q^{39} + 8 q^{41} + 4 q^{45} + 28 q^{47} + 104 q^{49} + 8 q^{51} + 16 q^{53} + 16 q^{55} - 4 q^{57} + 4 q^{59} + 20 q^{61} + 4 q^{63} + 40 q^{65} + 12 q^{67} + 16 q^{69} + 20 q^{71} + 8 q^{73} + 44 q^{77} + 8 q^{79} + 84 q^{81} - 8 q^{83} + 36 q^{85} + 32 q^{89} - 12 q^{91} - 12 q^{93} + 28 q^{95} + 12 q^{97} - 4 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6036))\) 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 3 503
6036.2.a.a 6036.a 1.a $1$ $48.198$ \(\Q\) None \(0\) \(-1\) \(-3\) \(3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-3q^{5}+3q^{7}+q^{9}+6q^{11}+\cdots\)
6036.2.a.b 6036.a 1.a $1$ $48.198$ \(\Q\) None \(0\) \(-1\) \(3\) \(1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+3q^{5}+q^{7}+q^{9}-2q^{11}-5q^{13}+\cdots\)
6036.2.a.c 6036.a 1.a $1$ $48.198$ \(\Q\) None \(0\) \(1\) \(-3\) \(-5\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-3q^{5}-5q^{7}+q^{9}-6q^{11}+\cdots\)
6036.2.a.d 6036.a 1.a $1$ $48.198$ \(\Q\) None \(0\) \(1\) \(-1\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+q^{7}+q^{9}+6q^{11}+3q^{13}+\cdots\)
6036.2.a.e 6036.a 1.a $1$ $48.198$ \(\Q\) None \(0\) \(1\) \(1\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+q^{7}+q^{9}-2q^{11}+3q^{13}+\cdots\)
6036.2.a.f 6036.a 1.a $14$ $48.198$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(-14\) \(-6\) \(-7\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-\beta _{1}q^{5}+\beta _{2}q^{7}+q^{9}+\beta _{3}q^{11}+\cdots\)
6036.2.a.g 6036.a 1.a $15$ $48.198$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(0\) \(15\) \(-11\) \(-4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+(-1+\beta _{1})q^{5}-\beta _{8}q^{7}+q^{9}+\cdots\)
6036.2.a.h 6036.a 1.a $24$ $48.198$ None \(0\) \(24\) \(18\) \(9\) $-$ $-$ $-$ $\mathrm{SU}(2)$
6036.2.a.i 6036.a 1.a $26$ $48.198$ None \(0\) \(-26\) \(6\) \(5\) $-$ $+$ $+$ $\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6036))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6036)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(503))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1006))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1509))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2012))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3018))\)\(^{\oplus 2}\)