Properties

Label 360.2.m
Level $360$
Weight $2$
Character orbit 360.m
Rep. character $\chi_{360}(179,\cdot)$
Character field $\Q$
Dimension $24$
Newform subspaces $3$
Sturm bound $144$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 360.m (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 120 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(144\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(360, [\chi])\).

Total New Old
Modular forms 80 24 56
Cusp forms 64 24 40
Eisenstein series 16 0 16

Trace form

\( 24q - 4q^{4} + O(q^{10}) \) \( 24q - 4q^{4} - 8q^{10} + 20q^{16} + 16q^{19} - 32q^{34} - 28q^{40} - 48q^{46} + 24q^{49} - 28q^{64} + 32q^{70} - 56q^{76} - 8q^{94} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(360, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
360.2.m.a \(4\) \(2.875\) \(\Q(\sqrt{-2}, \sqrt{-5})\) \(\Q(\sqrt{-10}) \) \(0\) \(0\) \(0\) \(-8\) \(q-\beta _{1}q^{2}-2q^{4}+\beta _{2}q^{5}+(-2+\beta _{3})q^{7}+\cdots\)
360.2.m.b \(4\) \(2.875\) \(\Q(\sqrt{-2}, \sqrt{-5})\) \(\Q(\sqrt{-10}) \) \(0\) \(0\) \(0\) \(8\) \(q-\beta _{1}q^{2}-2q^{4}+\beta _{2}q^{5}+(2-\beta _{3})q^{7}+\cdots\)
360.2.m.c \(16\) \(2.875\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+(1-\beta _{2})q^{4}-\beta _{12}q^{5}+(-\beta _{6}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(360, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(360, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 2}\)