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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
726.2.e.a \(4\) \(5.797\) \(\Q(\zeta_{10})\) None \(-1\) \(-1\) \(-5\) \(-3\) \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
726.2.e.b \(4\) \(5.797\) \(\Q(\zeta_{10})\) None \(-1\) \(-1\) \(0\) \(2\) \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
726.2.e.c \(4\) \(5.797\) \(\Q(\zeta_{10})\) None \(-1\) \(-1\) \(0\) \(2\) \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
726.2.e.d \(4\) \(5.797\) \(\Q(\zeta_{10})\) None \(-1\) \(-1\) \(1\) \(-4\) \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
726.2.e.e \(4\) \(5.797\) \(\Q(\zeta_{10})\) None \(-1\) \(-1\) \(4\) \(2\) \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
726.2.e.f \(4\) \(5.797\) \(\Q(\zeta_{10})\) None \(-1\) \(1\) \(-7\) \(-1\) \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
726.2.e.g \(4\) \(5.797\) \(\Q(\zeta_{10})\) None \(-1\) \(1\) \(-2\) \(4\) \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
726.2.e.h \(4\) \(5.797\) \(\Q(\zeta_{10})\) None \(-1\) \(1\) \(0\) \(0\) \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
726.2.e.i \(4\) \(5.797\) \(\Q(\zeta_{10})\) None \(-1\) \(1\) \(1\) \(4\) \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
726.2.e.j \(4\) \(5.797\) \(\Q(\zeta_{10})\) None \(1\) \(-1\) \(-5\) \(3\) \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+\zeta_{10}^{2}q^{3}+\cdots\)
726.2.e.k \(4\) \(5.797\) \(\Q(\zeta_{10})\) None \(1\) \(-1\) \(0\) \(-2\) \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+\zeta_{10}^{2}q^{3}+\cdots\)
726.2.e.l \(4\) \(5.797\) \(\Q(\zeta_{10})\) None \(1\) \(-1\) \(1\) \(4\) \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+\zeta_{10}^{2}q^{3}+\cdots\)
726.2.e.m \(4\) \(5.797\) \(\Q(\zeta_{10})\) None \(1\) \(-1\) \(4\) \(-2\) \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+\zeta_{10}^{2}q^{3}+\cdots\)
726.2.e.n \(4\) \(5.797\) \(\Q(\zeta_{10})\) None \(1\) \(1\) \(-7\) \(1\) \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-\zeta_{10}^{2}q^{3}+\cdots\)
726.2.e.o \(4\) \(5.797\) \(\Q(\zeta_{10})\) None \(1\) \(1\) \(-2\) \(-4\) \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-\zeta_{10}^{2}q^{3}+\cdots\)
726.2.e.p \(4\) \(5.797\) \(\Q(\zeta_{10})\) None \(1\) \(1\) \(0\) \(0\) \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-\zeta_{10}^{2}q^{3}+\cdots\)
726.2.e.q \(4\) \(5.797\) \(\Q(\zeta_{10})\) None \(1\) \(1\) \(1\) \(-4\) \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-\zeta_{10}^{2}q^{3}+\cdots\)
726.2.e.r \(4\) \(5.797\) \(\Q(\zeta_{10})\) None \(1\) \(1\) \(8\) \(6\) \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-\zeta_{10}^{2}q^{3}+\cdots\)

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

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