Properties

Label 722.2.e
Level $722$
Weight $2$
Character orbit 722.e
Rep. character $\chi_{722}(99,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $174$
Newform subspaces $19$
Sturm bound $190$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 722 = 2 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 722.e (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{9})\)
Newform subspaces: \( 19 \)
Sturm bound: \(190\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(3\), \(5\), \(7\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(722, [\chi])\).

Total New Old
Modular forms 690 174 516
Cusp forms 450 174 276
Eisenstein series 240 0 240

Trace form

\( 174q + 3q^{3} + 3q^{6} + 12q^{7} + 3q^{8} + 3q^{9} + O(q^{10}) \) \( 174q + 3q^{3} + 3q^{6} + 12q^{7} + 3q^{8} + 3q^{9} + 12q^{11} - 12q^{13} - 12q^{14} + 6q^{15} + 12q^{17} + 6q^{18} - 24q^{20} - 24q^{21} + 12q^{23} + 3q^{24} - 6q^{26} - 3q^{27} + 6q^{28} + 18q^{29} - 6q^{31} - 3q^{33} + 12q^{34} + 12q^{35} + 3q^{36} + 12q^{37} - 24q^{39} - 3q^{41} + 12q^{42} + 6q^{43} + 24q^{45} - 30q^{47} - 6q^{48} - 45q^{49} - 3q^{50} - 21q^{51} + 6q^{52} - 24q^{53} - 9q^{54} - 18q^{55} - 12q^{56} - 48q^{58} + 3q^{59} + 6q^{60} - 6q^{61} - 18q^{62} - 12q^{63} - 87q^{64} - 12q^{65} - 3q^{66} + 9q^{67} + 9q^{68} + 6q^{69} + 12q^{70} + 18q^{71} - 6q^{72} + 30q^{73} + 18q^{74} - 12q^{77} + 18q^{78} - 6q^{79} + 33q^{81} - 3q^{82} + 36q^{83} - 6q^{84} + 24q^{85} - 12q^{86} + 24q^{87} + 6q^{88} - 12q^{90} + 12q^{91} - 6q^{92} - 6q^{93} + 12q^{94} - 3q^{97} - 21q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(722, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
722.2.e.a \(6\) \(5.765\) \(\Q(\zeta_{18})\) None \(0\) \(-6\) \(0\) \(-6\) \(q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}+(-1-\zeta_{18}^{2}+\cdots)q^{3}+\cdots\)
722.2.e.b \(6\) \(5.765\) \(\Q(\zeta_{18})\) None \(0\) \(-3\) \(0\) \(-6\) \(q+(\zeta_{18}-\zeta_{18}^{4})q^{2}+(-1+\zeta_{18}^{3}-\zeta_{18}^{5})q^{3}+\cdots\)
722.2.e.c \(6\) \(5.765\) \(\Q(\zeta_{18})\) None \(0\) \(0\) \(0\) \(-9\) \(q+(\zeta_{18}-\zeta_{18}^{4})q^{2}+\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots\)
722.2.e.d \(6\) \(5.765\) \(\Q(\zeta_{18})\) None \(0\) \(0\) \(0\) \(-9\) \(q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}-\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots\)
722.2.e.e \(6\) \(5.765\) \(\Q(\zeta_{18})\) None \(0\) \(0\) \(0\) \(3\) \(q+(\zeta_{18}-\zeta_{18}^{4})q^{2}+\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots\)
722.2.e.f \(6\) \(5.765\) \(\Q(\zeta_{18})\) None \(0\) \(0\) \(0\) \(3\) \(q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}-\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots\)
722.2.e.g \(6\) \(5.765\) \(\Q(\zeta_{18})\) None \(0\) \(0\) \(0\) \(9\) \(q+(\zeta_{18}-\zeta_{18}^{4})q^{2}-3\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots\)
722.2.e.h \(6\) \(5.765\) \(\Q(\zeta_{18})\) None \(0\) \(0\) \(0\) \(9\) \(q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}+3\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots\)
722.2.e.i \(6\) \(5.765\) \(\Q(\zeta_{18})\) None \(0\) \(0\) \(0\) \(12\) \(q+(\zeta_{18}-\zeta_{18}^{4})q^{2}+\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots\)
722.2.e.j \(6\) \(5.765\) \(\Q(\zeta_{18})\) None \(0\) \(0\) \(0\) \(12\) \(q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}-\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots\)
722.2.e.k \(6\) \(5.765\) \(\Q(\zeta_{18})\) None \(0\) \(3\) \(0\) \(-6\) \(q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}+(\zeta_{18}^{2}+\zeta_{18}^{3}+\cdots)q^{3}+\cdots\)
722.2.e.l \(6\) \(5.765\) \(\Q(\zeta_{18})\) None \(0\) \(3\) \(0\) \(-6\) \(q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}+(1-\zeta_{18}^{3}+\zeta_{18}^{5})q^{3}+\cdots\)
722.2.e.m \(6\) \(5.765\) \(\Q(\zeta_{18})\) None \(0\) \(6\) \(0\) \(-6\) \(q+(\zeta_{18}-\zeta_{18}^{4})q^{2}+(1+\zeta_{18}^{2})q^{3}+\cdots\)
722.2.e.n \(12\) \(5.765\) 12.0.\(\cdots\).3 None \(0\) \(0\) \(0\) \(-6\) \(q+\beta _{10}q^{2}+(-\beta _{1}-\beta _{7})q^{3}+\beta _{2}q^{4}+\cdots\)
722.2.e.o \(12\) \(5.765\) 12.0.\(\cdots\).3 None \(0\) \(0\) \(0\) \(-6\) \(q-\beta _{10}q^{2}+(-\beta _{1}-\beta _{7})q^{3}+\beta _{2}q^{4}+\cdots\)
722.2.e.p \(12\) \(5.765\) 12.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(6\) \(q-\beta _{9}q^{2}-2\beta _{7}q^{3}-\beta _{11}q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
722.2.e.q \(12\) \(5.765\) 12.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(6\) \(q+(\beta _{3}-\beta _{9})q^{2}-2\beta _{1}q^{3}+(-\beta _{5}+\beta _{11})q^{4}+\cdots\)
722.2.e.r \(24\) \(5.765\) None \(0\) \(0\) \(0\) \(6\)
722.2.e.s \(24\) \(5.765\) None \(0\) \(0\) \(0\) \(6\)

Decomposition of \(S_{2}^{\mathrm{old}}(722, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(722, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(361, [\chi])\)\(^{\oplus 2}\)