Properties

Label 760.2.p
Level $760$
Weight $2$
Character orbit 760.p
Rep. character $\chi_{760}(379,\cdot)$
Character field $\Q$
Dimension $116$
Newform subspaces $9$
Sturm bound $240$
Trace bound $10$

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Defining parameters

Level: \( N \) \(=\) \( 760 = 2^{3} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 760.p (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 760 \)
Character field: \(\Q\)
Newform subspaces: \( 9 \)
Sturm bound: \(240\)
Trace bound: \(10\)
Distinguishing \(T_p\): \(3\), \(7\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(760, [\chi])\).

Total New Old
Modular forms 124 124 0
Cusp forms 116 116 0
Eisenstein series 8 8 0

Trace form

\( 116q - 8q^{4} - 16q^{6} + 100q^{9} + O(q^{10}) \) \( 116q - 8q^{4} - 16q^{6} + 100q^{9} - 8q^{11} - 8q^{16} + 4q^{19} - 12q^{20} - 4q^{25} + 16q^{26} - 8q^{30} - 40q^{36} + 16q^{44} + 84q^{49} - 56q^{54} - 56q^{64} - 64q^{66} - 40q^{74} - 32q^{80} + 52q^{81} - 16q^{96} - 136q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(760, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
760.2.p.a \(4\) \(6.069\) \(\Q(\sqrt{-2}, \sqrt{5})\) \(\Q(\sqrt{-10}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-2q^{4}-\beta _{3}q^{5}+2\beta _{3}q^{7}+\cdots\)
760.2.p.b \(4\) \(6.069\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}+\beta _{2})q^{2}-2\beta _{2}q^{3}+(-1-\beta _{3})q^{4}+\cdots\)
760.2.p.c \(4\) \(6.069\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}+\beta _{2})q^{2}-2\beta _{2}q^{3}+(-1-\beta _{3})q^{4}+\cdots\)
760.2.p.d \(8\) \(6.069\) 8.0.1499238400.2 None \(-8\) \(-8\) \(0\) \(0\) \(q+(-1-\beta _{5})q^{2}-q^{3}+2\beta _{5}q^{4}+(\beta _{5}+\cdots)q^{5}+\cdots\)
760.2.p.e \(8\) \(6.069\) 8.0.5473632256.3 None \(-4\) \(8\) \(0\) \(0\) \(q+\beta _{6}q^{2}+q^{3}+(-1-\beta _{3}-\beta _{4}-\beta _{6}+\cdots)q^{4}+\cdots\)
760.2.p.f \(8\) \(6.069\) 8.0.5473632256.3 None \(4\) \(-8\) \(0\) \(0\) \(q-\beta _{6}q^{2}-q^{3}+(-1-\beta _{3}-\beta _{4}-\beta _{6}+\cdots)q^{4}+\cdots\)
760.2.p.g \(8\) \(6.069\) 8.0.1499238400.2 None \(8\) \(8\) \(0\) \(0\) \(q+(1+\beta _{5})q^{2}+q^{3}+2\beta _{5}q^{4}+(-\beta _{4}+\cdots)q^{5}+\cdots\)
760.2.p.h \(16\) \(6.069\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) \(\Q(\sqrt{-95}) \) \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}-\beta _{7}q^{3}+\beta _{2}q^{4}+\beta _{4}q^{5}+\cdots\)
760.2.p.i \(56\) \(6.069\) None \(0\) \(0\) \(0\) \(0\)