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Properties

Label 2523.1.j
Level $2523$
Weight $1$
Character orbit 2523.j
Rep. character $\chi_{2523}(605,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $36$
Newform subspaces $3$
Sturm bound $290$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 2523 = 3 \cdot 29^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2523.j (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 87 \)
Character field: \(\Q(\zeta_{14})\)
Newform subspaces: \( 3 \)
Sturm bound: \(290\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2523, [\chi])\).

Total New Old
Modular forms 216 192 24
Cusp forms 36 36 0
Eisenstein series 180 156 24

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 36 0 0 0

Trace form

\( 36 q - 4 q^{4} - 2 q^{6} + 4 q^{7} - 2 q^{9} + O(q^{10}) \) \( 36 q - 4 q^{4} - 2 q^{6} + 4 q^{7} - 2 q^{9} - 2 q^{16} + 2 q^{22} - 2 q^{24} - 6 q^{25} - 12 q^{28} - 2 q^{33} + 2 q^{34} - 4 q^{36} + 2 q^{42} - 2 q^{49} - 2 q^{51} + 2 q^{52} + 2 q^{54} - 12 q^{57} - 2 q^{64} - 2 q^{78} - 6 q^{81} + 4 q^{82} - 12 q^{88} + 6 q^{91} + 2 q^{93} - 2 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(2523, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2523.1.j.a 2523.j 87.j $12$ $1.259$ 12.0.\(\cdots\).1 $D_{5}$ \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(0\) \(1\) \(q+\beta _{5}q^{3}+(-1-\beta _{3}-\beta _{5}+\beta _{7}+\beta _{9}+\cdots)q^{4}+\cdots\)
2523.1.j.b 2523.j 87.j $12$ $1.259$ \(\Q(\zeta_{28})\) $D_{3}$ \(\Q(\sqrt{-87}) \) None \(0\) \(0\) \(0\) \(2\) \(q+\zeta_{28}^{5}q^{2}+\zeta_{28}^{11}q^{3}-\zeta_{28}^{2}q^{6}+\cdots\)
2523.1.j.c 2523.j 87.j $12$ $1.259$ 12.0.\(\cdots\).1 $D_{5}$ \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(0\) \(1\) \(q-\beta _{5}q^{3}+(-1-\beta _{3}-\beta _{5}+\beta _{7}+\beta _{9}+\cdots)q^{4}+\cdots\)