Properties

Label 3525.1.bd
Level $3525$
Weight $1$
Character orbit 3525.bd
Rep. character $\chi_{3525}(101,\cdot)$
Character field $\Q(\zeta_{46})$
Dimension $44$
Newform subspaces $1$
Sturm bound $480$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 3525 = 3 \cdot 5^{2} \cdot 47 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3525.bd (of order \(46\) and degree \(22\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 141 \)
Character field: \(\Q(\zeta_{46})\)
Newform subspaces: \( 1 \)
Sturm bound: \(480\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3525, [\chi])\).

Total New Old
Modular forms 308 176 132
Cusp forms 44 44 0
Eisenstein series 264 132 132

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 44 0 0 0

Trace form

\( 44 q + 6 q^{4} - 4 q^{6} + 2 q^{9} + O(q^{10}) \) \( 44 q + 6 q^{4} - 4 q^{6} + 2 q^{9} - 10 q^{16} + 4 q^{19} + 8 q^{24} - 4 q^{31} + 8 q^{34} - 6 q^{36} - 8 q^{46} + 2 q^{49} - 4 q^{51} + 4 q^{54} - 4 q^{61} + 14 q^{64} + 4 q^{69} + 34 q^{76} + 4 q^{79} - 2 q^{81} - 42 q^{94} + 34 q^{96} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3525, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3525.1.bd.a 3525.bd 141.h $44$ $1.759$ \(\Q(\zeta_{92})\) $D_{23}$ \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{92}^{3}-\zeta_{92}^{25})q^{2}+\zeta_{92}^{13}q^{3}+\cdots\)