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Properties

Label 3325.1.bc
Level $3325$
Weight $1$
Character orbit 3325.bc
Rep. character $\chi_{3325}(2876,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $4$
Newform subspaces $1$
Sturm bound $400$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 3325 = 5^{2} \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3325.bc (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 133 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(400\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3325, [\chi])\).

Total New Old
Modular forms 40 16 24
Cusp forms 16 4 12
Eisenstein series 24 12 12

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 0 4 0 0

Trace form

\( 4 q + 2 q^{2} + 4 q^{8} + O(q^{10}) \) \( 4 q + 2 q^{2} + 4 q^{8} + 2 q^{16} + 2 q^{21} + 2 q^{23} + 2 q^{29} - 4 q^{39} - 2 q^{42} + 2 q^{43} + 4 q^{46} - 4 q^{49} + 2 q^{51} - 2 q^{53} + 2 q^{57} + 4 q^{58} + 4 q^{64} + 2 q^{67} + 2 q^{71} - 2 q^{78} - 2 q^{79} + 2 q^{81} - 2 q^{86} + 2 q^{91} - 2 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(3325, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3325.1.bc.a 3325.bc 133.m $4$ $1.659$ \(\Q(\zeta_{12})\) $A_{4}$ None None 133.1.m.a \(2\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{2}q^{2}+\zeta_{12}^{5}q^{3}-\zeta_{12}q^{6}-\zeta_{12}^{3}q^{7}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3325, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3325, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(133, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(665, [\chi])\)\(^{\oplus 2}\)