Properties

Label 72.2.n
Level $72$
Weight $2$
Character orbit 72.n
Rep. character $\chi_{72}(13,\cdot)$
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.n (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

\( 20q - q^{2} - q^{4} - q^{6} - 2q^{7} - 10q^{8} - 4q^{9} + O(q^{10}) \) \( 20q - q^{2} - q^{4} - q^{6} - 2q^{7} - 10q^{8} - 4q^{9} - 8q^{10} - 16q^{12} + 8q^{14} - 10q^{15} - q^{16} - 8q^{17} + 16q^{18} - 16q^{20} - 5q^{22} - 14q^{23} - 5q^{24} + 20q^{26} + 4q^{28} + 34q^{30} - 2q^{31} + 19q^{32} - 18q^{33} - 9q^{34} + 27q^{36} + 25q^{38} + 2q^{39} - 2q^{40} + 2q^{41} + 8q^{42} + 42q^{44} - 12q^{46} + 18q^{47} + 39q^{48} - 25q^{50} - 47q^{54} - 28q^{55} + 26q^{56} + 4q^{57} - 14q^{58} + 6q^{60} - 68q^{62} + 50q^{63} + 26q^{64} - 22q^{65} - 72q^{66} - 39q^{68} - 16q^{70} + 48q^{71} - 65q^{72} - 8q^{73} - 34q^{74} + 9q^{76} - 2q^{78} - 2q^{79} - 96q^{80} - 8q^{81} + 18q^{82} - 76q^{84} + 29q^{86} + 42q^{87} + 19q^{88} + 8q^{89} + 52q^{90} - 30q^{92} + 40q^{95} - 26q^{96} - 2q^{97} + 102q^{98} + O(q^{100}) \)

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.n.a \(4\) \(0.575\) \(\Q(\zeta_{12})\) None \(-2\) \(0\) \(0\) \(-8\) \(q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\cdots)q^{3}+\cdots\)
72.2.n.b \(16\) \(0.575\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(1\) \(0\) \(0\) \(6\) \(q+\beta _{6}q^{2}+(-\beta _{3}-\beta _{10})q^{3}+(\beta _{8}-\beta _{13}+\cdots)q^{4}+\cdots\)