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Properties

Label 1476.1.z
Level $1476$
Weight $1$
Character orbit 1476.z
Rep. character $\chi_{1476}(127,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $4$
Newform subspaces $1$
Sturm bound $252$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1476 = 2^{2} \cdot 3^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1476.z (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 164 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 1 \)
Sturm bound: \(252\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 48 12 36
Cusp forms 16 4 12
Eisenstein series 32 8 24

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

\( 4 q + q^{2} - q^{4} - 2 q^{5} + q^{8} + O(q^{10}) \) \( 4 q + q^{2} - q^{4} - 2 q^{5} + q^{8} + 2 q^{10} - q^{16} + 3 q^{20} - 3 q^{25} + 5 q^{26} - 4 q^{32} + 5 q^{34} - 3 q^{37} + 2 q^{40} + q^{41} + q^{49} - 2 q^{50} + 5 q^{52} - 2 q^{61} - q^{64} - 5 q^{65} + 2 q^{73} + 3 q^{74} + 3 q^{80} - q^{82} - 5 q^{97} - q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1476.1.z.a 1476.z 164.l $4$ $0.737$ \(\Q(\zeta_{10})\) $D_{10}$ \(\Q(\sqrt{-1}) \) None \(1\) \(0\) \(-2\) \(0\) \(q+\zeta_{10}^{3}q^{2}-\zeta_{10}q^{4}+(-\zeta_{10}^{3}+\zeta_{10}^{4}+\cdots)q^{5}+\cdots\)

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

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