Properties

Label 3675.1.u
Level $3675$
Weight $1$
Character orbit 3675.u
Rep. character $\chi_{3675}(851,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $32$
Newform subspaces $6$
Sturm bound $560$
Trace bound $18$

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Defining parameters

Level: \( N \) \(=\) \( 3675 = 3 \cdot 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3675.u (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 6 \)
Sturm bound: \(560\)
Trace bound: \(18\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3675, [\chi])\).

Total New Old
Modular forms 136 56 80
Cusp forms 40 32 8
Eisenstein series 96 24 72

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

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

Trace form

\( 32 q + 4 q^{9} + O(q^{10}) \) \( 32 q + 4 q^{9} + 8 q^{16} - 2 q^{19} + 4 q^{31} + 8 q^{36} - 6 q^{39} + 12 q^{51} - 2 q^{61} + 4 q^{76} + 6 q^{79} + 16 q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3675, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3675.1.u.a 3675.u 21.h $2$ $1.834$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(0\) \(q-\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{9}+\zeta_{6}^{2}q^{12}+\cdots\)
3675.1.u.b 3675.u 21.h $2$ $1.834$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(0\) \(q+\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{9}-\zeta_{6}^{2}q^{12}+\cdots\)
3675.1.u.c 3675.u 21.h $4$ $1.834$ \(\Q(\zeta_{12})\) $D_{2}$ \(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-35}) \) \(\Q(\sqrt{21}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{3}+\zeta_{12}^{4}q^{4}+\zeta_{12}^{2}q^{9}-\zeta_{12}^{5}q^{12}+\cdots\)
3675.1.u.d 3675.u 21.h $8$ $1.834$ \(\Q(\zeta_{24})\) $S_{4}$ None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{10}q^{2}+\zeta_{24}^{11}q^{3}-\zeta_{24}^{9}q^{6}+\cdots\)
3675.1.u.e 3675.u 21.h $8$ $1.834$ \(\Q(\zeta_{24})\) $S_{4}$ None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{10}q^{2}-\zeta_{24}^{5}q^{3}+\zeta_{24}^{3}q^{6}+\cdots\)
3675.1.u.f 3675.u 21.h $8$ $1.834$ \(\Q(\zeta_{24})\) $D_{4}$ \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{24}+\zeta_{24}^{7})q^{2}-\zeta_{24}^{2}q^{3}-\zeta_{24}^{8}q^{4}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3675, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3675, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 2}\)