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Properties

Label 726.2.i
Level $726$
Weight $2$
Character orbit 726.i
Rep. character $\chi_{726}(67,\cdot)$
Character field $\Q(\zeta_{11})$
Dimension $220$
Newform subspaces $4$
Sturm bound $264$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 726 = 2 \cdot 3 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 726.i (of order \(11\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 121 \)
Character field: \(\Q(\zeta_{11})\)
Newform subspaces: \( 4 \)
Sturm bound: \(264\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 1360 220 1140
Cusp forms 1280 220 1060
Eisenstein series 80 0 80

Trace form

\( 220q - 22q^{4} + 8q^{5} + 2q^{6} + 12q^{7} + 220q^{9} + O(q^{10}) \) \( 220q - 22q^{4} + 8q^{5} + 2q^{6} + 12q^{7} + 220q^{9} - 14q^{10} - 32q^{11} - 68q^{13} - 28q^{14} + 12q^{15} - 22q^{16} + 24q^{17} + 20q^{19} + 8q^{20} + 4q^{21} - 34q^{22} + 16q^{23} + 2q^{24} + 6q^{25} + 8q^{26} + 12q^{28} + 8q^{29} + 12q^{30} - 16q^{31} + 10q^{33} + 8q^{34} + 48q^{35} - 22q^{36} - 92q^{37} + 8q^{38} + 8q^{39} - 36q^{40} + 40q^{41} + 4q^{42} + 28q^{43} + 12q^{44} + 8q^{45} + 32q^{46} + 56q^{47} - 66q^{49} + 16q^{50} + 28q^{51} + 20q^{52} - 4q^{53} + 2q^{54} + 28q^{55} + 16q^{56} + 28q^{57} - 32q^{58} + 40q^{59} + 12q^{60} + 76q^{61} + 48q^{62} + 12q^{63} - 22q^{64} - 20q^{65} + 8q^{66} - 156q^{67} + 24q^{68} + 24q^{69} - 4q^{70} - 16q^{71} + 40q^{73} + 24q^{74} + 16q^{75} - 24q^{76} + 88q^{77} - 72q^{79} + 8q^{80} + 220q^{81} - 4q^{82} + 88q^{83} + 4q^{84} - 80q^{85} + 40q^{86} + 20q^{87} + 10q^{88} - 24q^{89} - 14q^{90} - 52q^{91} - 28q^{92} + 16q^{93} - 296q^{94} + 112q^{95} + 2q^{96} - 56q^{97} + 48q^{98} - 32q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.i.a \(50\) \(5.797\) None \(-5\) \(50\) \(10\) \(9\)
726.2.i.b \(50\) \(5.797\) None \(5\) \(-50\) \(0\) \(-1\)
726.2.i.c \(60\) \(5.797\) None \(-6\) \(-60\) \(-2\) \(5\)
726.2.i.d \(60\) \(5.797\) None \(6\) \(60\) \(0\) \(-1\)

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

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