Properties

Label 2007.1.d
Level $2007$
Weight $1$
Character orbit 2007.d
Rep. character $\chi_{2007}(1783,\cdot)$
Character field $\Q$
Dimension $10$
Newform subspaces $3$
Sturm bound $224$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 2007 = 3^{2} \cdot 223 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2007.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 223 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(224\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2007, [\chi])\).

Total New Old
Modular forms 23 11 12
Cusp forms 19 10 9
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 10 0 0 0

Trace form

\( 10 q + q^{2} + 9 q^{4} - q^{7} + 2 q^{8} + O(q^{10}) \) \( 10 q + q^{2} + 9 q^{4} - q^{7} + 2 q^{8} + 2 q^{14} + 8 q^{16} + q^{17} - q^{19} + 10 q^{25} - 3 q^{28} + q^{29} - q^{31} + 3 q^{32} - 2 q^{34} - q^{37} + 2 q^{38} + q^{41} - q^{43} + q^{47} + 9 q^{49} + q^{50} + q^{53} - 3 q^{56} - 9 q^{58} - 5 q^{62} + 7 q^{64} - 4 q^{68} - q^{73} + 2 q^{74} - 10 q^{76} - 2 q^{82} + q^{83} - 5 q^{86} + q^{89} - 2 q^{94} - 4 q^{98} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2007, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2007.1.d.a 2007.d 223.b $1$ $1.002$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-223}) \) \(\Q(\sqrt{669}) \) \(0\) \(0\) \(0\) \(-2\) \(q-q^{4}-2q^{7}+q^{16}+2q^{19}+q^{25}+\cdots\)
2007.1.d.b 2007.d 223.b $3$ $1.002$ \(\Q(\zeta_{14})^+\) $D_{7}$ \(\Q(\sqrt{-223}) \) None \(1\) \(0\) \(0\) \(-1\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1+\beta _{1}-\beta _{2})q^{7}+\cdots\)
2007.1.d.c 2007.d 223.b $6$ $1.002$ \(\Q(\zeta_{28})^+\) $D_{14}$ \(\Q(\sqrt{-223}) \) None \(0\) \(0\) \(0\) \(2\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1-\beta _{2}-\beta _{4}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2007, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2007, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(223, [\chi])\)\(^{\oplus 3}\)