Properties

Label 1872.1.bb
Level $1872$
Weight $1$
Character orbit 1872.bb
Rep. character $\chi_{1872}(883,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $8$
Newform subspaces $1$
Sturm bound $336$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1872 = 2^{4} \cdot 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1872.bb (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 208 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(336\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1872, [\chi])\).

Total New Old
Modular forms 24 12 12
Cusp forms 8 8 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 8 0 0 0

Trace form

\( 8 q + O(q^{10}) \) \( 8 q - 8 q^{22} - 8 q^{43} + 8 q^{49} + 8 q^{52} - 16 q^{55} + 8 q^{88} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1872, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1872.1.bb.a 1872.bb 208.o $8$ $0.934$ \(\Q(\zeta_{16})\) $D_{8}$ \(\Q(\sqrt{-39}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{16}^{5}q^{2}-\zeta_{16}^{2}q^{4}+(\zeta_{16}^{5}+\zeta_{16}^{7}+\cdots)q^{5}+\cdots\)