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Properties

Label 1476.1.o
Level $1476$
Weight $1$
Character orbit 1476.o
Rep. character $\chi_{1476}(655,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $16$
Newform subspaces $4$
Sturm bound $252$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 1476 = 2^{2} \cdot 3^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1476.o (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1476 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 4 \)
Sturm bound: \(252\)
Trace bound: \(3\)

Dimensions

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

Total New Old
Modular forms 24 24 0
Cusp forms 16 16 0
Eisenstein series 8 8 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 16 0 0 0

Trace form

\( 16 q - 8 q^{4} + O(q^{10}) \) \( 16 q - 8 q^{4} - 8 q^{16} - 8 q^{25} - 8 q^{41} + 16 q^{42} - 8 q^{45} - 8 q^{49} + 8 q^{50} - 8 q^{57} + 16 q^{64} - 8 q^{66} + 8 q^{77} - 8 q^{90} + O(q^{100}) \)

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.o.a 1476.o 1476.o $2$ $0.737$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-41}) \) None \(-1\) \(-2\) \(1\) \(-1\) \(q+\zeta_{6}^{2}q^{2}-q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{5}-\zeta_{6}^{2}q^{6}+\cdots\)
1476.1.o.b 1476.o 1476.o $2$ $0.737$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-41}) \) None \(-1\) \(2\) \(1\) \(1\) \(q+\zeta_{6}^{2}q^{2}+q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+\zeta_{6}^{2}q^{6}+\cdots\)
1476.1.o.c 1476.o 1476.o $4$ $0.737$ \(\Q(\zeta_{12})\) $D_{6}$ \(\Q(\sqrt{-41}) \) None \(-2\) \(0\) \(-2\) \(0\) \(q-\zeta_{12}^{2}q^{2}-\zeta_{12}^{3}q^{3}+\zeta_{12}^{4}q^{4}+\cdots\)
1476.1.o.d 1476.o 1476.o $8$ $0.737$ \(\Q(\zeta_{24})\) $D_{12}$ \(\Q(\sqrt{-41}) \) None \(4\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{4}q^{2}+\zeta_{24}^{9}q^{3}+\zeta_{24}^{8}q^{4}+\cdots\)