Properties

Label 360.2.d
Level $360$
Weight $2$
Character orbit 360.d
Rep. character $\chi_{360}(109,\cdot)$
Character field $\Q$
Dimension $28$
Newform subspaces $6$
Sturm bound $144$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 360.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(144\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\)

Dimensions

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

Total New Old
Modular forms 80 32 48
Cusp forms 64 28 36
Eisenstein series 16 4 12

Trace form

\( 28q + O(q^{10}) \) \( 28q - 4q^{10} + 8q^{14} + 12q^{16} - 8q^{20} - 4q^{25} + 28q^{26} + 8q^{34} - 20q^{40} + 8q^{41} - 20q^{44} + 28q^{46} - 20q^{49} - 24q^{50} - 8q^{55} - 52q^{56} - 36q^{64} + 24q^{65} - 28q^{70} + 16q^{71} - 12q^{74} - 24q^{76} - 32q^{79} + 36q^{80} - 52q^{86} + 16q^{89} + 4q^{94} - 40q^{95} + O(q^{100}) \)

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.d.a \(4\) \(2.875\) \(\Q(\sqrt{-2}, \sqrt{-5})\) \(\Q(\sqrt{-30}) \) \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}-2q^{4}+\beta _{2}q^{5}+2\beta _{1}q^{8}+\cdots\)
360.2.d.b \(4\) \(2.875\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-1+\beta _{3})q^{4}+(-\beta _{2}+\beta _{3})q^{5}+\cdots\)
360.2.d.c \(4\) \(2.875\) \(\Q(\sqrt{-3}, \sqrt{5})\) \(\Q(\sqrt{-15}) \) \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}+\beta _{3}q^{4}+(-\beta _{1}-\beta _{2})q^{5}+\cdots\)
360.2.d.d \(4\) \(2.875\) \(\Q(\sqrt{2}, \sqrt{-3})\) \(\Q(\sqrt{-6}) \) \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+2q^{4}+(\beta _{1}+\beta _{2})q^{5}+2\beta _{3}q^{7}+\cdots\)
360.2.d.e \(6\) \(2.875\) 6.0.839056.1 None \(-1\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{2}+(-\beta _{1}-\beta _{2})q^{4}+(\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
360.2.d.f \(6\) \(2.875\) 6.0.839056.1 None \(1\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}+(\beta _{1}-\beta _{3})q^{4}+(\beta _{2}-\beta _{3})q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(360, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 2}\)