Properties

Label 72.2.l
Level $72$
Weight $2$
Character orbit 72.l
Rep. character $\chi_{72}(11,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $20$
Newform subspaces $2$
Sturm bound $24$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 72 = 2^{3} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 72.l (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 72 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(24\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(72, [\chi])\).

Total New Old
Modular forms 28 28 0
Cusp forms 20 20 0
Eisenstein series 8 8 0

Trace form

\( 20q - 3q^{2} - 4q^{3} - q^{4} - 7q^{6} - 4q^{9} + O(q^{10}) \) \( 20q - 3q^{2} - 4q^{3} - q^{4} - 7q^{6} - 4q^{9} - 6q^{11} + 2q^{12} - 18q^{14} - q^{16} - 16q^{18} - 8q^{19} + 18q^{20} - 5q^{22} + 29q^{24} - 4q^{25} - 16q^{27} - 12q^{28} + 12q^{30} + 27q^{32} - 2q^{33} - 5q^{34} + 23q^{36} + 21q^{38} - 12q^{40} - 18q^{41} + 42q^{42} - 2q^{43} + 12q^{46} - 19q^{48} - 4q^{49} + 51q^{50} + 28q^{51} - 18q^{52} + 35q^{54} - 66q^{56} - 20q^{57} + 12q^{58} + 30q^{59} - 72q^{60} + 2q^{64} - 6q^{65} - 32q^{66} - 2q^{67} - 45q^{68} + 18q^{70} - 37q^{72} - 8q^{73} - 60q^{74} + 68q^{75} - 11q^{76} - 72q^{78} + 8q^{81} + 10q^{82} + 54q^{83} + 12q^{84} - 87q^{86} - 5q^{88} - 66q^{90} - 36q^{91} + 84q^{92} + 24q^{94} + 74q^{96} - 2q^{97} + 10q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(72, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
72.2.l.a \(4\) \(0.575\) \(\Q(\sqrt{-2}, \sqrt{-3})\) \(\Q(\sqrt{-2}) \) \(0\) \(2\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+2\beta _{2}q^{4}+\cdots\)
72.2.l.b \(16\) \(0.575\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-3\) \(-6\) \(0\) \(0\) \(q-\beta _{11}q^{2}+(-\beta _{3}+\beta _{6})q^{3}+(-1-\beta _{1}+\cdots)q^{4}+\cdots\)