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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
60.2.h.a \(4\) \(0.479\) \(\Q(\sqrt{-2}, \sqrt{-5})\) \(\Q(\sqrt{-5}) \) \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}-\beta _{1}q^{3}-2q^{4}-\beta _{3}q^{5}+(-1+\cdots)q^{6}+\cdots\)
60.2.h.b \(4\) \(0.479\) \(\Q(\sqrt{-3}, \sqrt{5})\) \(\Q(\sqrt{-15}) \) \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+\beta _{3}q^{4}+\cdots\)