Properties

Label 360.1.u
Level $360$
Weight $1$
Character orbit 360.u
Rep. character $\chi_{360}(37,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $4$
Newform subspaces $1$
Sturm bound $72$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 360.u (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(72\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(360, [\chi])\).

Total New Old
Modular forms 20 8 12
Cusp forms 4 4 0
Eisenstein series 16 4 12

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 4 0 0 0

Trace form

\( 4 q - 4 q^{7} + O(q^{10}) \) \( 4 q - 4 q^{7} + 4 q^{10} - 4 q^{16} + 4 q^{22} - 4 q^{28} - 4 q^{55} - 4 q^{58} - 4 q^{70} + 4 q^{73} + 4 q^{88} - 4 q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(360, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
360.1.u.a 360.u 40.i $4$ $0.180$ \(\Q(\zeta_{8})\) $D_{4}$ \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(-4\) \(q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+\zeta_{8}q^{5}+(-1+\cdots)q^{7}+\cdots\)