Properties

Label 1520.2.d
Level $1520$
Weight $2$
Character orbit 1520.d
Rep. character $\chi_{1520}(609,\cdot)$
Character field $\Q$
Dimension $54$
Newform subspaces $11$
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.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 11 \)
Sturm bound: \(480\)
Trace bound: \(15\)
Distinguishing \(T_p\): \(3\), \(7\)

Dimensions

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

Total New Old
Modular forms 252 54 198
Cusp forms 228 54 174
Eisenstein series 24 0 24

Trace form

\( 54q + 2q^{5} - 54q^{9} + O(q^{10}) \) \( 54q + 2q^{5} - 54q^{9} - 12q^{11} + 12q^{15} + 6q^{19} - 8q^{21} + 10q^{25} + 4q^{29} - 6q^{35} - 40q^{39} - 4q^{41} - 10q^{45} - 70q^{49} + 24q^{51} + 10q^{55} + 16q^{59} + 20q^{61} - 8q^{65} + 8q^{69} + 8q^{71} + 28q^{75} + 62q^{81} - 8q^{85} + 12q^{89} - 16q^{91} + 28q^{99} + O(q^{100}) \)

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.d.a \(2\) \(12.137\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+iq^{3}+(-1-i)q^{5}+iq^{7}-q^{9}+\cdots\)
1520.2.d.b \(2\) \(12.137\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+(-1-i)q^{5}-iq^{7}+3q^{9}+4q^{11}+\cdots\)
1520.2.d.c \(4\) \(12.137\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(-4\) \(0\) \(q+\beta _{1}q^{3}+(-1-\beta _{2})q^{5}+(2\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
1520.2.d.d \(4\) \(12.137\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{8}+\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+(2\zeta_{8}-\zeta_{8}^{3})q^{5}+\cdots\)
1520.2.d.e \(4\) \(12.137\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{8}+\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+(-2\zeta_{8}-\zeta_{8}^{3})q^{5}+\cdots\)
1520.2.d.f \(4\) \(12.137\) \(\Q(\sqrt{-2}, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+\beta _{2}q^{5}+(\beta _{1}-\beta _{3})q^{7}+\beta _{2}q^{9}+\cdots\)
1520.2.d.g \(4\) \(12.137\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(4\) \(0\) \(q+\zeta_{8}^{2}q^{3}+(1-\zeta_{8})q^{5}+(-\zeta_{8}-2\zeta_{8}^{2}+\cdots)q^{7}+\cdots\)
1520.2.d.h \(6\) \(12.137\) 6.0.16516096.1 None \(0\) \(0\) \(-1\) \(0\) \(q-\beta _{4}q^{3}+\beta _{3}q^{5}+(\beta _{1}+\beta _{4})q^{7}+(-3+\cdots)q^{9}+\cdots\)
1520.2.d.i \(6\) \(12.137\) 6.0.14077504.2 None \(0\) \(0\) \(-1\) \(0\) \(q+\beta _{2}q^{3}+\beta _{5}q^{5}+(-\beta _{3}-\beta _{4})q^{7}+\cdots\)
1520.2.d.j \(6\) \(12.137\) 6.0.5161984.1 None \(0\) \(0\) \(2\) \(0\) \(q+\beta _{5}q^{3}+(\beta _{2}+\beta _{3})q^{5}+(-\beta _{4}+\beta _{5})q^{7}+\cdots\)
1520.2.d.k \(12\) \(12.137\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(6\) \(0\) \(q-\beta _{11}q^{3}-\beta _{6}q^{5}+(\beta _{5}+\beta _{11})q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1520, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(380, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(760, [\chi])\)\(^{\oplus 2}\)