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Properties

Label 726.2.e
Level $726$
Weight $2$
Character orbit 726.e
Rep. character $\chi_{726}(487,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $72$
Newform subspaces $18$
Sturm bound $264$
Trace bound $10$

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Defining parameters

Level: \( N \) \(=\) \( 726 = 2 \cdot 3 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 726.e (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 18 \)
Sturm bound: \(264\)
Trace bound: \(10\)
Distinguishing \(T_p\): \(5\), \(7\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(726, [\chi])\).

Total New Old
Modular forms 624 72 552
Cusp forms 432 72 360
Eisenstein series 192 0 192

Trace form

\( 72 q - 18 q^{4} - 8 q^{5} - 2 q^{6} + 8 q^{7} - 18 q^{9} + O(q^{10}) \) \( 72 q - 18 q^{4} - 8 q^{5} - 2 q^{6} + 8 q^{7} - 18 q^{9} + 12 q^{10} + 4 q^{14} - 2 q^{15} - 18 q^{16} + 16 q^{17} - 20 q^{19} - 8 q^{20} + 16 q^{21} + 16 q^{23} - 2 q^{24} - 6 q^{25} - 16 q^{26} - 2 q^{28} + 12 q^{29} - 12 q^{30} - 6 q^{31} + 24 q^{34} - 28 q^{35} - 18 q^{36} - 28 q^{37} - 16 q^{38} - 8 q^{39} + 2 q^{40} - 20 q^{41} - 2 q^{42} + 32 q^{43} - 8 q^{45} - 12 q^{46} - 46 q^{49} + 24 q^{50} + 12 q^{51} + 4 q^{53} + 8 q^{54} - 16 q^{56} + 12 q^{57} - 18 q^{58} + 4 q^{59} + 8 q^{60} + 4 q^{61} + 12 q^{62} + 8 q^{63} - 18 q^{64} + 8 q^{65} + 64 q^{67} + 16 q^{68} - 12 q^{69} + 14 q^{70} + 6 q^{73} + 16 q^{74} - 32 q^{75} + 20 q^{79} + 12 q^{80} - 18 q^{81} - 24 q^{82} - 28 q^{83} - 4 q^{84} + 24 q^{85} + 12 q^{86} - 20 q^{87} + 32 q^{89} - 8 q^{90} + 40 q^{91} - 24 q^{92} + 60 q^{93} - 16 q^{94} - 52 q^{95} - 2 q^{96} + 44 q^{97} - 48 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(726, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
726.2.e.a 726.e 11.c $4$ $5.797$ \(\Q(\zeta_{10})\) None \(-1\) \(-1\) \(-5\) \(-3\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
726.2.e.b 726.e 11.c $4$ $5.797$ \(\Q(\zeta_{10})\) None \(-1\) \(-1\) \(0\) \(2\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
726.2.e.c 726.e 11.c $4$ $5.797$ \(\Q(\zeta_{10})\) None \(-1\) \(-1\) \(0\) \(2\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
726.2.e.d 726.e 11.c $4$ $5.797$ \(\Q(\zeta_{10})\) None \(-1\) \(-1\) \(1\) \(-4\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
726.2.e.e 726.e 11.c $4$ $5.797$ \(\Q(\zeta_{10})\) None \(-1\) \(-1\) \(4\) \(2\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
726.2.e.f 726.e 11.c $4$ $5.797$ \(\Q(\zeta_{10})\) None \(-1\) \(1\) \(-7\) \(-1\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
726.2.e.g 726.e 11.c $4$ $5.797$ \(\Q(\zeta_{10})\) None \(-1\) \(1\) \(-2\) \(4\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
726.2.e.h 726.e 11.c $4$ $5.797$ \(\Q(\zeta_{10})\) None \(-1\) \(1\) \(0\) \(0\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
726.2.e.i 726.e 11.c $4$ $5.797$ \(\Q(\zeta_{10})\) None \(-1\) \(1\) \(1\) \(4\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
726.2.e.j 726.e 11.c $4$ $5.797$ \(\Q(\zeta_{10})\) None \(1\) \(-1\) \(-5\) \(3\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+\zeta_{10}^{2}q^{3}+\cdots\)
726.2.e.k 726.e 11.c $4$ $5.797$ \(\Q(\zeta_{10})\) None \(1\) \(-1\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+\zeta_{10}^{2}q^{3}+\cdots\)
726.2.e.l 726.e 11.c $4$ $5.797$ \(\Q(\zeta_{10})\) None \(1\) \(-1\) \(1\) \(4\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+\zeta_{10}^{2}q^{3}+\cdots\)
726.2.e.m 726.e 11.c $4$ $5.797$ \(\Q(\zeta_{10})\) None \(1\) \(-1\) \(4\) \(-2\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+\zeta_{10}^{2}q^{3}+\cdots\)
726.2.e.n 726.e 11.c $4$ $5.797$ \(\Q(\zeta_{10})\) None \(1\) \(1\) \(-7\) \(1\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-\zeta_{10}^{2}q^{3}+\cdots\)
726.2.e.o 726.e 11.c $4$ $5.797$ \(\Q(\zeta_{10})\) None \(1\) \(1\) \(-2\) \(-4\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-\zeta_{10}^{2}q^{3}+\cdots\)
726.2.e.p 726.e 11.c $4$ $5.797$ \(\Q(\zeta_{10})\) None \(1\) \(1\) \(0\) \(0\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-\zeta_{10}^{2}q^{3}+\cdots\)
726.2.e.q 726.e 11.c $4$ $5.797$ \(\Q(\zeta_{10})\) None \(1\) \(1\) \(1\) \(-4\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-\zeta_{10}^{2}q^{3}+\cdots\)
726.2.e.r 726.e 11.c $4$ $5.797$ \(\Q(\zeta_{10})\) None \(1\) \(1\) \(8\) \(6\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-\zeta_{10}^{2}q^{3}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(726, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(726, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(66, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(121, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(242, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(363, [\chi])\)\(^{\oplus 2}\)