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Properties

Label 352.1.t
Level $352$
Weight $1$
Character orbit 352.t
Rep. character $\chi_{352}(15,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $4$
Newform subspaces $1$
Sturm bound $48$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 352 = 2^{5} \cdot 11 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 352.t (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 88 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 1 \)
Sturm bound: \(48\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(352, [\chi])\).

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

\( 4 q + 2 q^{3} - 3 q^{9} + O(q^{10}) \) \( 4 q + 2 q^{3} - 3 q^{9} + q^{11} - 2 q^{17} - 3 q^{19} - q^{25} - q^{27} + 3 q^{33} - 2 q^{41} + 2 q^{43} - q^{49} - q^{51} + q^{57} - 3 q^{59} + 2 q^{67} - 2 q^{73} - 3 q^{75} - 3 q^{83} - 2 q^{89} + 3 q^{97} + 3 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(352, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
352.1.t.a 352.t 88.l $4$ $0.176$ \(\Q(\zeta_{10})\) $D_{5}$ \(\Q(\sqrt{-2}) \) None \(0\) \(2\) \(0\) \(0\) \(q+(\zeta_{10}^{3}-\zeta_{10}^{4})q^{3}+(-\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(352, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(352, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(88, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(176, [\chi])\)\(^{\oplus 2}\)