Properties

Label 2700.1.t
Level $2700$
Weight $1$
Character orbit 2700.t
Rep. character $\chi_{2700}(451,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $4$
Newform subspaces $1$
Sturm bound $540$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 2700 = 2^{2} \cdot 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2700.t (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 36 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(540\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2700, [\chi])\).

Total New Old
Modular forms 84 16 68
Cusp forms 12 4 8
Eisenstein series 72 12 60

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

\( 4 q + 2 q^{4} + O(q^{10}) \) \( 4 q + 2 q^{4} + 2 q^{14} - 2 q^{16} + 2 q^{29} - 2 q^{41} - 4 q^{46} - 2 q^{56} + 2 q^{61} - 4 q^{64} + 4 q^{86} - 4 q^{89} - 2 q^{94} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2700, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2700.1.t.a 2700.t 36.f $4$ $1.347$ \(\Q(\zeta_{12})\) $D_{3}$ \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}q^{7}-\zeta_{12}^{3}q^{8}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2700, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2700, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(900, [\chi])\)\(^{\oplus 2}\)