Properties

Label 2700.1.b
Level $2700$
Weight $1$
Character orbit 2700.b
Rep. character $\chi_{2700}(1349,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $2$
Sturm bound $540$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 2700 = 2^{2} \cdot 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2700.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(540\)
Trace bound: \(19\)

Dimensions

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

Total New Old
Modular forms 82 4 78
Cusp forms 28 4 24
Eisenstein series 54 0 54

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

\( 4 q + O(q^{10}) \) \( 4 q - 2 q^{19} + 2 q^{31} - 6 q^{49} + 2 q^{61} + 4 q^{79} - 2 q^{91} + O(q^{100}) \)

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.b.a 2700.b 15.d $2$ $1.347$ \(\Q(\sqrt{-1}) \) $D_{3}$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{7}-iq^{13}-q^{19}-q^{31}+iq^{37}+\cdots\)
2700.1.b.b 2700.b 15.d $2$ $1.347$ \(\Q(\sqrt{-1}) \) $D_{3}$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{7}+iq^{13}+q^{19}+q^{31}-iq^{37}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(2700, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(675, [\chi])\)\(^{\oplus 3}\)