Properties

Label 2700.1.c
Level $2700$
Weight $1$
Character orbit 2700.c
Rep. character $\chi_{2700}(1351,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $2$
Sturm bound $540$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 2700 = 2^{2} \cdot 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2700.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(540\)
Trace bound: \(2\)

Dimensions

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

Total New Old
Modular forms 44 4 40
Cusp forms 8 4 4
Eisenstein series 36 0 36

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

\( 4 q - 2 q^{4} + O(q^{10}) \) \( 4 q - 2 q^{4} - 2 q^{16} - 2 q^{34} - 6 q^{46} + 4 q^{49} + 4 q^{61} + 4 q^{64} - 6 q^{76} + O(q^{100}) \)

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

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2700.1.c.a \(2\) \(1.347\) \(\Q(\sqrt{-3}) \) \(D_{6}\) \(\Q(\sqrt{-15}) \) None \(-1\) \(0\) \(0\) \(0\) \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+q^{8}+\zeta_{6}^{2}q^{16}+\cdots\)
2700.1.c.b \(2\) \(1.347\) \(\Q(\sqrt{-3}) \) \(D_{6}\) \(\Q(\sqrt{-15}) \) None \(1\) \(0\) \(0\) \(0\) \(q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-q^{8}+\zeta_{6}^{2}q^{16}+\cdots\)

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

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