Properties

Label 2100.1.bh
Level $2100$
Weight $1$
Character orbit 2100.bh
Rep. character $\chi_{2100}(149,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $8$
Newform subspaces $2$
Sturm bound $480$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2100.bh (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 105 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(480\)
Trace bound: \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2100, [\chi])\).

Total New Old
Modular forms 92 8 84
Cusp forms 20 8 12
Eisenstein series 72 0 72

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

\( 8 q + 4 q^{9} + O(q^{10}) \) \( 8 q + 4 q^{9} + 2 q^{19} + 2 q^{21} + 4 q^{31} + 2 q^{39} - 2 q^{49} - 2 q^{61} - 4 q^{79} - 4 q^{81} + 10 q^{91} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2100, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2100.1.bh.a 2100.bh 105.o $4$ $1.048$ \(\Q(\zeta_{12})\) $D_{3}$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{3}+\zeta_{12}^{5}q^{7}+\zeta_{12}^{2}q^{9}-\zeta_{12}^{3}q^{13}+\cdots\)
2100.1.bh.b 2100.bh 105.o $4$ $1.048$ \(\Q(\zeta_{12})\) $D_{3}$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{3}-\zeta_{12}^{3}q^{7}+\zeta_{12}^{2}q^{9}+\zeta_{12}^{3}q^{13}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2100, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2100, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 3}\)