Properties

Label 60.2.h
Level $60$
Weight $2$
Character orbit 60.h
Rep. character $\chi_{60}(59,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $2$
Sturm bound $24$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 60.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 60 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(24\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(60, [\chi])\).

Total New Old
Modular forms 16 16 0
Cusp forms 8 8 0
Eisenstein series 8 8 0

Trace form

\( 8 q - 6 q^{4} + 2 q^{6} - 4 q^{9} + O(q^{10}) \) \( 8 q - 6 q^{4} + 2 q^{6} - 4 q^{9} - 10 q^{10} + 2 q^{16} - 20 q^{21} + 26 q^{24} + 20 q^{30} + 20 q^{34} - 22 q^{36} + 10 q^{40} + 20 q^{45} - 4 q^{46} - 16 q^{49} - 46 q^{54} - 30 q^{60} + 24 q^{61} - 54 q^{64} + 28 q^{69} - 40 q^{70} + 60 q^{76} + 32 q^{81} + 40 q^{84} - 40 q^{85} + 30 q^{90} + 92 q^{94} - 22 q^{96} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(60, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
60.2.h.a 60.h 60.h $4$ $0.479$ \(\Q(\sqrt{-2}, \sqrt{-5})\) \(\Q(\sqrt{-5}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{2}q^{2}-\beta _{1}q^{3}-2q^{4}-\beta _{3}q^{5}+(-1+\cdots)q^{6}+\cdots\)
60.2.h.b 60.h 60.h $4$ $0.479$ \(\Q(\sqrt{-3}, \sqrt{5})\) \(\Q(\sqrt{-15}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{2}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+\beta _{3}q^{4}+\cdots\)