Properties

Label 900.1.c
Level $900$
Weight $1$
Character orbit 900.c
Rep. character $\chi_{900}(451,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $2$
Sturm bound $180$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 900.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(180\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(900, [\chi])\).

Total New Old
Modular forms 26 5 21
Cusp forms 2 2 0
Eisenstein series 24 3 21

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 2 0 0 0

Trace form

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

Decomposition of \(S_{1}^{\mathrm{new}}(900, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
900.1.c.a \(1\) \(0.449\) \(\Q\) \(D_{2}\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-15}) \) \(\Q(\sqrt{15}) \) \(-1\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}-q^{8}+q^{16}+2q^{17}-q^{32}+\cdots\)
900.1.c.b \(1\) \(0.449\) \(\Q\) \(D_{2}\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-15}) \) \(\Q(\sqrt{15}) \) \(1\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}+q^{8}+q^{16}-2q^{17}+q^{32}+\cdots\)