Properties

Label 3600.1.bo
Level $3600$
Weight $1$
Character orbit 3600.bo
Rep. character $\chi_{3600}(451,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $4$
Newform subspaces $1$
Sturm bound $720$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3600 = 2^{4} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3600.bo (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(720\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3600, [\chi])\).

Total New Old
Modular forms 52 10 42
Cusp forms 4 4 0
Eisenstein series 48 6 42

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

\( 4 q + O(q^{10}) \) \( 4 q - 4 q^{16} - 4 q^{19} + 4 q^{34} + 4 q^{46} - 4 q^{49} - 4 q^{61} - 4 q^{76} - 4 q^{94} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3600, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3600.1.bo.a 3600.bo 16.f $4$ $1.797$ \(\Q(\zeta_{8})\) $D_{4}$ \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{8}-q^{16}+\cdots\)