Properties

Label 726.2.a
Level $726$
Weight $2$
Character orbit 726.a
Rep. character $\chi_{726}(1,\cdot)$
Character field $\Q$
Dimension $17$
Newform subspaces $13$
Sturm bound $264$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 726 = 2 \cdot 3 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 726.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 13 \)
Sturm bound: \(264\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\), \(7\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(726))\).

Total New Old
Modular forms 156 17 139
Cusp forms 109 17 92
Eisenstein series 47 0 47

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

\(2\)\(3\)\(11\)FrickeDim
\(+\)\(+\)\(+\)$+$\(1\)
\(+\)\(+\)\(-\)$-$\(4\)
\(+\)\(-\)\(+\)$-$\(2\)
\(+\)\(-\)\(-\)$+$\(2\)
\(-\)\(+\)\(+\)$-$\(3\)
\(-\)\(+\)\(-\)$+$\(1\)
\(-\)\(-\)\(-\)$-$\(4\)
Plus space\(+\)\(4\)
Minus space\(-\)\(13\)

Trace form

\( 17 q - q^{2} - q^{3} + 17 q^{4} + 2 q^{5} + q^{6} + 4 q^{7} - q^{8} + 17 q^{9} + O(q^{10}) \) \( 17 q - q^{2} - q^{3} + 17 q^{4} + 2 q^{5} + q^{6} + 4 q^{7} - q^{8} + 17 q^{9} + 2 q^{10} - q^{12} + 6 q^{13} + 8 q^{14} + 6 q^{15} + 17 q^{16} + 6 q^{17} - q^{18} + 2 q^{20} - 4 q^{21} + q^{24} + 15 q^{25} + 2 q^{26} - q^{27} + 4 q^{28} - 22 q^{29} + 6 q^{30} + 4 q^{31} - q^{32} - 2 q^{34} + 17 q^{36} + 10 q^{37} - 4 q^{38} - 6 q^{39} + 2 q^{40} - 2 q^{41} + 4 q^{42} - 16 q^{43} + 2 q^{45} + 8 q^{46} + 32 q^{47} - q^{48} + 29 q^{49} - 15 q^{50} + 10 q^{51} + 6 q^{52} + 2 q^{53} + q^{54} + 8 q^{56} + 8 q^{57} - 2 q^{58} - 4 q^{59} + 6 q^{60} + 14 q^{61} + 16 q^{62} + 4 q^{63} + 17 q^{64} + 28 q^{65} + 28 q^{67} + 6 q^{68} + 8 q^{69} + 8 q^{70} + 8 q^{71} - q^{72} + 10 q^{73} - 14 q^{74} + q^{75} - 14 q^{78} - 20 q^{79} + 2 q^{80} + 17 q^{81} + 22 q^{82} + 4 q^{83} - 4 q^{84} - 12 q^{85} + 4 q^{86} - 10 q^{87} - 2 q^{89} + 2 q^{90} - 72 q^{91} - 72 q^{93} + 8 q^{94} - 8 q^{95} + q^{96} - 62 q^{97} - 9 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(726))\) 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 11
726.2.a.a 726.a 1.a $1$ $5.797$ \(\Q\) None \(-1\) \(-1\) \(-1\) \(4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+4q^{7}+\cdots\)
726.2.a.b 726.a 1.a $1$ $5.797$ \(\Q\) None \(-1\) \(-1\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\)
726.2.a.c 726.a 1.a $1$ $5.797$ \(\Q\) None \(-1\) \(-1\) \(2\) \(4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}+4q^{7}+\cdots\)
726.2.a.d 726.a 1.a $1$ $5.797$ \(\Q\) None \(-1\) \(1\) \(-4\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-4q^{5}-q^{6}+2q^{7}+\cdots\)
726.2.a.e 726.a 1.a $1$ $5.797$ \(\Q\) None \(-1\) \(1\) \(-1\) \(-4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-4q^{7}+\cdots\)
726.2.a.f 726.a 1.a $1$ $5.797$ \(\Q\) None \(1\) \(-1\) \(-1\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-4q^{7}+\cdots\)
726.2.a.g 726.a 1.a $1$ $5.797$ \(\Q\) None \(1\) \(-1\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots\)
726.2.a.h 726.a 1.a $1$ $5.797$ \(\Q\) None \(1\) \(1\) \(-1\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+4q^{7}+\cdots\)
726.2.a.i 726.a 1.a $1$ $5.797$ \(\Q\) None \(1\) \(1\) \(0\) \(-2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}-2q^{7}+q^{8}+\cdots\)
726.2.a.j 726.a 1.a $2$ $5.797$ \(\Q(\sqrt{5}) \) None \(-2\) \(-2\) \(-1\) \(-7\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+(1-3\beta )q^{5}+q^{6}+\cdots\)
726.2.a.k 726.a 1.a $2$ $5.797$ \(\Q(\sqrt{5}) \) None \(-2\) \(2\) \(5\) \(-1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+(3-\beta )q^{5}-q^{6}+\cdots\)
726.2.a.l 726.a 1.a $2$ $5.797$ \(\Q(\sqrt{5}) \) None \(2\) \(-2\) \(-1\) \(7\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(1-3\beta )q^{5}-q^{6}+\cdots\)
726.2.a.m 726.a 1.a $2$ $5.797$ \(\Q(\sqrt{5}) \) None \(2\) \(2\) \(5\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(3-\beta )q^{5}+q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(726))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(726)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(242))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(363))\)\(^{\oplus 2}\)