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Properties

Label 927.1.d
Level $927$
Weight $1$
Character orbit 927.d
Rep. character $\chi_{927}(514,\cdot)$
Character field $\Q$
Dimension $7$
Newform subspaces $3$
Sturm bound $104$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 927 = 3^{2} \cdot 103 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 927.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 103 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(104\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(927, [\chi])\).

Total New Old
Modular forms 17 8 9
Cusp forms 13 7 6
Eisenstein series 4 1 3

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 7 0 0 0

Trace form

\( 7 q + q^{2} + 6 q^{4} - q^{7} + 2 q^{8} + O(q^{10}) \) \( 7 q + q^{2} + 6 q^{4} - q^{7} + 2 q^{8} - q^{13} + 2 q^{14} + 5 q^{16} + q^{17} - q^{19} + q^{23} + 7 q^{25} - 3 q^{26} - 8 q^{28} + q^{29} - 2 q^{32} - 2 q^{34} - 3 q^{38} + q^{41} - 7 q^{46} + 6 q^{49} + q^{50} - 3 q^{52} - q^{56} - 2 q^{58} + q^{59} - q^{61} + 4 q^{64} - 2 q^{68} - 3 q^{76} - q^{79} - 7 q^{82} + q^{83} - 2 q^{91} + 3 q^{92} - q^{97} - 2 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(927, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
927.1.d.a 927.d 103.b $1$ $0.463$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-103}) \) \(\Q(\sqrt{309}) \) \(0\) \(0\) \(0\) \(2\) \(q-q^{4}+2q^{7}-2q^{13}+q^{16}+2q^{19}+\cdots\)
927.1.d.b 927.d 103.b $2$ $0.463$ \(\Q(\sqrt{5}) \) $D_{5}$ \(\Q(\sqrt{-103}) \) None \(1\) \(0\) \(0\) \(-1\) \(q+(1-\beta )q^{2}+(1-\beta )q^{4}-\beta q^{7}+q^{8}+\cdots\)
927.1.d.c 927.d 103.b $4$ $0.463$ \(\Q(\zeta_{20})^+\) $D_{10}$ \(\Q(\sqrt{-103}) \) None \(0\) \(0\) \(0\) \(-2\) \(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-1-\beta _{2})q^{7}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(927, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(927, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(103, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(309, [\chi])\)\(^{\oplus 2}\)