Properties

Label 1519.1.c
Level $1519$
Weight $1$
Character orbit 1519.c
Rep. character $\chi_{1519}(1177,\cdot)$
Character field $\Q$
Dimension $7$
Newform subspaces $3$
Sturm bound $149$
Trace bound $10$

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Defining parameters

Level: \( N \) \(=\) \( 1519 = 7^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1519.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 31 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(149\)
Trace bound: \(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1519, [\chi])\).

Total New Old
Modular forms 18 12 6
Cusp forms 10 7 3
Eisenstein series 8 5 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

\( 7 q - q^{2} + 6 q^{4} + q^{5} - 5 q^{8} + 7 q^{9} + O(q^{10}) \) \( 7 q - q^{2} + 6 q^{4} + q^{5} - 5 q^{8} + 7 q^{9} - q^{10} + 5 q^{16} - q^{18} + q^{19} + 6 q^{25} - q^{31} - 6 q^{32} + 6 q^{36} - q^{38} + q^{40} + q^{41} + q^{45} - 2 q^{47} - 6 q^{50} + q^{59} + q^{62} + q^{64} - 4 q^{67} - q^{71} - 5 q^{72} - q^{80} + 7 q^{81} - q^{82} - q^{90} + 2 q^{94} - 5 q^{95} + q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1519, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1519.1.c.a 1519.c 31.b $1$ $0.758$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-31}) \) None \(-1\) \(0\) \(1\) \(0\) \(q-q^{2}+q^{5}+q^{8}+q^{9}-q^{10}-q^{16}+\cdots\)
1519.1.c.b 1519.c 31.b $3$ $0.758$ \(\Q(\zeta_{18})^+\) $D_{9}$ \(\Q(\sqrt{-31}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}-\beta _{2})q^{2}+(1-\beta _{1})q^{4}-\beta _{1}q^{5}+\cdots\)
1519.1.c.c 1519.c 31.b $3$ $0.758$ \(\Q(\zeta_{18})^+\) $D_{9}$ \(\Q(\sqrt{-31}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}-\beta _{2})q^{2}+(1-\beta _{1})q^{4}+\beta _{1}q^{5}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1519, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1519, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(31, [\chi])\)\(^{\oplus 3}\)