Properties

Label 1520.2.g
Level $1520$
Weight $2$
Character orbit 1520.g
Rep. character $\chi_{1520}(1519,\cdot)$
Character field $\Q$
Dimension $60$
Newform subspaces $7$
Sturm bound $480$
Trace bound $15$

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Defining parameters

Level: \( N \) \(=\) \( 1520 = 2^{4} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1520.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 380 \)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(480\)
Trace bound: \(15\)
Distinguishing \(T_p\): \(3\), \(7\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1520, [\chi])\).

Total New Old
Modular forms 252 60 192
Cusp forms 228 60 168
Eisenstein series 24 0 24

Trace form

\( 60 q - 60 q^{9} + O(q^{10}) \) \( 60 q - 60 q^{9} + 84 q^{49} - 36 q^{81} - 60 q^{85} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1520, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1520.2.g.a \(2\) \(12.137\) \(\Q(\sqrt{-19}) \) \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(-1\) \(-6\) \(q-\beta q^{5}-3q^{7}+3q^{9}+(1-2\beta )q^{11}+\cdots\)
1520.2.g.b \(2\) \(12.137\) \(\Q(\sqrt{-19}) \) \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(-1\) \(6\) \(q+(-1+\beta )q^{5}+3q^{7}+3q^{9}+(1-2\beta )q^{11}+\cdots\)
1520.2.g.c \(4\) \(12.137\) \(\Q(\sqrt{-3}, \sqrt{-19})\) \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(1\) \(-6\) \(q-\beta _{3}q^{5}+(-2-\beta _{1}-\beta _{3})q^{7}+3q^{9}+\cdots\)
1520.2.g.d \(4\) \(12.137\) \(\Q(\sqrt{-3}, \sqrt{-19})\) \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(1\) \(6\) \(q-\beta _{1}q^{5}+(2+\beta _{1}+\beta _{3})q^{7}+3q^{9}+\cdots\)
1520.2.g.e \(16\) \(12.137\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{6}q^{3}-\beta _{14}q^{5}-\beta _{10}q^{7}+(-2+\cdots)q^{9}+\cdots\)
1520.2.g.f \(16\) \(12.137\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{4}q^{3}+(-\beta _{1}+\beta _{2})q^{5}+\beta _{8}q^{7}+\cdots\)
1520.2.g.g \(16\) \(12.137\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{6}q^{3}+\beta _{15}q^{5}+\beta _{10}q^{7}+(-2+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1520, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1520, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(380, [\chi])\)\(^{\oplus 3}\)