Properties

Label 1520.1.m
Level $1520$
Weight $1$
Character orbit 1520.m
Rep. character $\chi_{1520}(1329,\cdot)$
Character field $\Q$
Dimension $5$
Newform subspaces $3$
Sturm bound $240$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 1520 = 2^{4} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1520.m (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(240\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1520, [\chi])\).

Total New Old
Modular forms 38 7 31
Cusp forms 26 5 21
Eisenstein series 12 2 10

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 5 0 0 0

Trace form

\( 5 q - 2 q^{5} - q^{9} + O(q^{10}) \) \( 5 q - 2 q^{5} - q^{9} - q^{19} + 2 q^{25} + 3 q^{35} + 4 q^{39} - 2 q^{45} - q^{49} + 3 q^{55} + q^{81} + 3 q^{85} - 2 q^{95} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1520, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1520.1.m.a 1520.m 95.d $1$ $0.759$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-95}) \) \(\Q(\sqrt{5}) \) 95.1.d.a \(0\) \(0\) \(1\) \(0\) \(q+q^{5}-q^{9}+2q^{11}-q^{19}+q^{25}+\cdots\)
1520.1.m.b 1520.m 95.d $2$ $0.759$ \(\Q(\sqrt{2}) \) $D_{4}$ \(\Q(\sqrt{-95}) \) None 95.1.d.b \(0\) \(0\) \(-2\) \(0\) \(q-\beta q^{3}-q^{5}+q^{9}-\beta q^{13}+\beta q^{15}+\cdots\)
1520.1.m.c 1520.m 95.d $2$ $0.759$ \(\Q(\sqrt{-3}) \) $D_{6}$ \(\Q(\sqrt{-19}) \) None 380.1.g.a \(0\) \(0\) \(-1\) \(0\) \(q-\zeta_{6}q^{5}+(\zeta_{6}+\zeta_{6}^{2})q^{7}-q^{9}-q^{11}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1520, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1520, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(380, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(760, [\chi])\)\(^{\oplus 2}\)