Properties

Label 360.2.k
Level $360$
Weight $2$
Character orbit 360.k
Rep. character $\chi_{360}(181,\cdot)$
Character field $\Q$
Dimension $20$
Newform subspaces $6$
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.k (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(144\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(7\), \(11\), \(17\)

Dimensions

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

Total New Old
Modular forms 80 20 60
Cusp forms 64 20 44
Eisenstein series 16 0 16

Trace form

\( 20q - 2q^{2} + 4q^{4} - 4q^{7} + 4q^{8} + O(q^{10}) \) \( 20q - 2q^{2} + 4q^{4} - 4q^{7} + 4q^{8} - 2q^{10} + 16q^{14} - 4q^{16} + 4q^{20} - 12q^{22} + 20q^{23} - 20q^{25} - 16q^{26} - 4q^{28} + 8q^{31} - 12q^{32} + 12q^{34} + 20q^{38} - 4q^{40} + 8q^{41} - 20q^{44} - 4q^{46} - 20q^{47} + 36q^{49} + 2q^{50} - 56q^{52} - 8q^{55} - 4q^{56} + 48q^{58} - 40q^{62} + 4q^{64} - 8q^{68} + 16q^{70} + 8q^{71} - 16q^{73} - 24q^{74} + 16q^{76} - 16q^{79} - 16q^{80} + 4q^{86} + 16q^{88} - 8q^{89} + 60q^{92} - 52q^{94} - 16q^{95} + 16q^{97} - 6q^{98} + O(q^{100}) \)

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.k.a \(2\) \(2.875\) \(\Q(\sqrt{-1}) \) None \(-2\) \(0\) \(0\) \(-8\) \(q+(-1+i)q^{2}-2iq^{4}+iq^{5}-4q^{7}+\cdots\)
360.2.k.b \(2\) \(2.875\) \(\Q(\sqrt{-1}) \) None \(-2\) \(0\) \(0\) \(4\) \(q+(-1+i)q^{2}-2iq^{4}+iq^{5}+2q^{7}+\cdots\)
360.2.k.c \(2\) \(2.875\) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(0\) \(-8\) \(q+(1+i)q^{2}+2iq^{4}+iq^{5}-4q^{7}+\cdots\)
360.2.k.d \(4\) \(2.875\) \(\Q(i, \sqrt{7})\) None \(0\) \(0\) \(0\) \(8\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{3}q^{5}+2q^{7}+\cdots\)
360.2.k.e \(4\) \(2.875\) \(\Q(\zeta_{12})\) None \(2\) \(0\) \(0\) \(-4\) \(q+(\zeta_{12}-\zeta_{12}^{2})q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{4}+\cdots\)
360.2.k.f \(6\) \(2.875\) 6.0.399424.1 None \(-2\) \(0\) \(0\) \(4\) \(q-\beta _{1}q^{2}+(\beta _{2}-\beta _{3})q^{4}+\beta _{3}q^{5}+(1+\cdots)q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(360, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 2}\)