↑

Properties

Label 327.1.d
Level $327$
Weight $1$
Character orbit 327.d
Rep. character $\chi_{327}(326,\cdot)$
Character field $\Q$
Dimension $5$
Newform subspaces $4$
Sturm bound $36$
Trace bound $2$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 327 = 3 \cdot 109 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 327.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 327 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(36\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(327, [\chi])\).

Total New Old
Modular forms 7 7 0
Cusp forms 5 5 0
Eisenstein series 2 2 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 5 0 0 0

Trace form

\( 5 q - q^{3} + 3 q^{4} - 2 q^{7} + 5 q^{9} + O(q^{10}) \) \( 5 q - q^{3} + 3 q^{4} - 2 q^{7} + 5 q^{9} - 3 q^{12} + q^{16} - 2 q^{21} - 4 q^{22} + 5 q^{25} - q^{27} - 6 q^{28} - 2 q^{31} - 4 q^{34} + 3 q^{36} - 2 q^{43} - 4 q^{46} - 5 q^{48} + 3 q^{49} - 2 q^{61} - 2 q^{63} - q^{64} - 4 q^{66} - 2 q^{73} - q^{75} + 5 q^{81} + 8 q^{82} + 6 q^{84} + 4 q^{88} - 2 q^{93} + 8 q^{94} - 2 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(327, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
327.1.d.a 327.d 327.d $1$ $0.163$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-327}) \) None \(-1\) \(1\) \(0\) \(-1\) \(q-q^{2}+q^{3}-q^{6}-q^{7}+q^{8}+q^{9}+\cdots\)
327.1.d.b 327.d 327.d $1$ $0.163$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-327}) \) \(\Q(\sqrt{109}) \) \(0\) \(-1\) \(0\) \(2\) \(q-q^{3}-q^{4}+2q^{7}+q^{9}+q^{12}+q^{16}+\cdots\)
327.1.d.c 327.d 327.d $1$ $0.163$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-327}) \) None \(1\) \(1\) \(0\) \(-1\) \(q+q^{2}+q^{3}+q^{6}-q^{7}-q^{8}+q^{9}+\cdots\)
327.1.d.d 327.d 327.d $2$ $0.163$ \(\Q(\sqrt{3}) \) $D_{6}$ \(\Q(\sqrt{-327}) \) None \(0\) \(-2\) \(0\) \(-2\) \(q-\beta q^{2}-q^{3}+2q^{4}+\beta q^{6}-q^{7}-\beta q^{8}+\cdots\)