Properties

Label 1476.1.h
Level $1476$
Weight $1$
Character orbit 1476.h
Rep. character $\chi_{1476}(163,\cdot)$
Character field $\Q$
Dimension $3$
Newform subspaces $2$
Sturm bound $252$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 1476 = 2^{2} \cdot 3^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1476.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 164 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(252\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1476, [\chi])\).

Total New Old
Modular forms 20 5 15
Cusp forms 12 3 9
Eisenstein series 8 2 6

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 3 0 0 0

Trace form

\( 3 q + q^{2} + 3 q^{4} + 2 q^{5} + q^{8} + O(q^{10}) \) \( 3 q + q^{2} + 3 q^{4} + 2 q^{5} + q^{8} - 2 q^{10} + 3 q^{16} + 2 q^{20} + q^{25} + q^{32} - 2 q^{37} - 2 q^{40} - 3 q^{41} + q^{49} - 5 q^{50} - 2 q^{61} + 3 q^{64} - 2 q^{73} + 2 q^{74} - 4 q^{77} + 2 q^{80} - q^{82} + 3 q^{98} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1476, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1476.1.h.a \(1\) \(0.737\) \(\Q\) \(D_{2}\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-41}) \) \(\Q(\sqrt{41}) \) \(-1\) \(0\) \(2\) \(0\) \(q-q^{2}+q^{4}+2q^{5}-q^{8}-2q^{10}+q^{16}+\cdots\)
1476.1.h.b \(2\) \(0.737\) \(\Q(\sqrt{2}) \) \(D_{4}\) \(\Q(\sqrt{-41}) \) None \(2\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}-\beta q^{7}+q^{8}+\beta q^{11}-\beta q^{14}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1476, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1476, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(164, [\chi])\)\(^{\oplus 3}\)