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Properties

Label 2023.1.c
Level $2023$
Weight $1$
Character orbit 2023.c
Rep. character $\chi_{2023}(1735,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $5$
Sturm bound $204$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 2023 = 7 \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2023.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(204\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2023, [\chi])\).

Total New Old
Modular forms 30 27 3
Cusp forms 12 12 0
Eisenstein series 18 15 3

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 12 0 0 0

Trace form

\( 12 q + 8 q^{4} + 6 q^{9} + O(q^{10}) \) \( 12 q + 8 q^{4} + 6 q^{9} + 4 q^{15} + 4 q^{16} - 8 q^{18} - 2 q^{21} + 6 q^{25} + 2 q^{30} - 10 q^{32} - 2 q^{35} - 6 q^{42} + 4 q^{49} + 2 q^{50} + 2 q^{60} - 4 q^{67} + 4 q^{70} - 6 q^{72} - 2 q^{77} + 8 q^{81} - 6 q^{84} + 2 q^{86} + 4 q^{93} - 4 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(2023, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2023.1.c.a 2023.c 7.b $1$ $1.010$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-7}) \) None \(-1\) \(0\) \(0\) \(-1\) \(q-q^{2}-q^{7}+q^{8}+q^{9}-2q^{11}+q^{14}+\cdots\)
2023.1.c.b 2023.c 7.b $1$ $1.010$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-7}) \) None \(-1\) \(0\) \(0\) \(1\) \(q-q^{2}+q^{7}+q^{8}+q^{9}+2q^{11}-q^{14}+\cdots\)
2023.1.c.c 2023.c 7.b $3$ $1.010$ \(\Q(\zeta_{18})^+\) $D_{9}$ \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(-3\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{7}+(-1-\beta _{1}+\cdots)q^{8}+\cdots\)
2023.1.c.d 2023.c 7.b $3$ $1.010$ \(\Q(\zeta_{18})^+\) $D_{9}$ \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(3\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{7}+(-1-\beta _{1}+\cdots)q^{8}+\cdots\)
2023.1.c.e 2023.c 7.b $4$ $1.010$ \(\Q(i, \sqrt{5})\) $D_{5}$ \(\Q(\sqrt{-119}) \) None \(2\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}-\beta _{1}q^{3}-\beta _{2}q^{4}+(\beta _{1}+\beta _{3})q^{5}+\cdots\)