Properties

Label 69.2.e
Level $69$
Weight $2$
Character orbit 69.e
Rep. character $\chi_{69}(4,\cdot)$
Character field $\Q(\zeta_{11})$
Dimension $40$
Newform subspaces $3$
Sturm bound $16$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 69 = 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 69.e (of order \(11\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 23 \)
Character field: \(\Q(\zeta_{11})\)
Newform subspaces: \( 3 \)
Sturm bound: \(16\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(69, [\chi])\).

Total New Old
Modular forms 100 40 60
Cusp forms 60 40 20
Eisenstein series 40 0 40

Trace form

\( 40q - 4q^{2} - 12q^{4} - 4q^{5} - 4q^{6} - 8q^{7} - 12q^{8} - 4q^{9} + O(q^{10}) \) \( 40q - 4q^{2} - 12q^{4} - 4q^{5} - 4q^{6} - 8q^{7} - 12q^{8} - 4q^{9} - 8q^{10} - 24q^{11} - 8q^{13} - 12q^{14} - 8q^{15} + 16q^{16} + 10q^{17} - 4q^{18} - 10q^{19} + 52q^{20} - 4q^{21} + 4q^{22} + 20q^{23} - 12q^{24} + 16q^{25} - 12q^{26} + 24q^{28} - 10q^{29} - 28q^{30} - 10q^{31} - 24q^{32} - 8q^{33} - 26q^{34} - 12q^{35} + 10q^{36} + 4q^{37} + 58q^{38} + 36q^{39} - 58q^{40} + 4q^{41} + 78q^{42} - 12q^{43} + 50q^{44} - 4q^{45} + 20q^{46} + 48q^{47} + 56q^{48} - 52q^{49} + 46q^{50} + 12q^{51} + 6q^{52} + 8q^{53} + 18q^{54} + 2q^{55} - 6q^{56} + 32q^{57} - 6q^{58} - 12q^{59} - 26q^{60} - 12q^{61} - 120q^{62} - 8q^{63} - 20q^{64} - 64q^{65} - 40q^{66} - 42q^{67} - 92q^{68} - 20q^{69} - 56q^{70} - 64q^{71} - 12q^{72} - 34q^{73} - 74q^{74} - 24q^{75} + 30q^{76} - 8q^{77} - 16q^{78} + 36q^{79} + 10q^{80} - 4q^{81} + 8q^{82} - 16q^{83} - 52q^{84} + 114q^{85} + 48q^{86} - 32q^{87} + 8q^{88} + 56q^{89} - 8q^{90} + 72q^{91} + 30q^{92} - 40q^{93} + 54q^{94} + 78q^{95} - 24q^{96} + 36q^{97} + 116q^{98} - 2q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(69, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
69.2.e.a \(10\) \(0.551\) \(\Q(\zeta_{22})\) None \(-4\) \(1\) \(5\) \(-8\) \(q+(-1+\zeta_{22}-\zeta_{22}^{2}-\zeta_{22}^{4}-\zeta_{22}^{6}+\cdots)q^{2}+\cdots\)
69.2.e.b \(10\) \(0.551\) \(\Q(\zeta_{22})\) None \(4\) \(1\) \(-3\) \(6\) \(q+(-\zeta_{22}^{4}+\zeta_{22}^{5}-\zeta_{22}^{8}+\zeta_{22}^{9})q^{2}+\cdots\)
69.2.e.c \(20\) \(0.551\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-4\) \(-2\) \(-6\) \(-6\) \(q+(\beta _{1}+\beta _{3}-\beta _{4}+\beta _{5}+2\beta _{6}+2\beta _{7}+\cdots)q^{2}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(69, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(69, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 2}\)