Properties

Label 1560.2.l
Level $1560$
Weight $2$
Character orbit 1560.l
Rep. character $\chi_{1560}(1249,\cdot)$
Character field $\Q$
Dimension $36$
Newform subspaces $6$
Sturm bound $672$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1560.l (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(672\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1560, [\chi])\).

Total New Old
Modular forms 352 36 316
Cusp forms 320 36 284
Eisenstein series 32 0 32

Trace form

\( 36 q - 36 q^{9} + O(q^{10}) \) \( 36 q - 36 q^{9} - 4 q^{15} + 24 q^{19} + 8 q^{21} - 20 q^{25} + 8 q^{31} - 8 q^{35} - 12 q^{49} - 40 q^{55} - 32 q^{59} + 16 q^{71} + 8 q^{79} + 36 q^{81} - 8 q^{85} + 16 q^{89} - 24 q^{91} + 8 q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1560, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1560.2.l.a \(2\) \(12.457\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+iq^{3}+(-1+2i)q^{5}+5iq^{7}-q^{9}+\cdots\)
1560.2.l.b \(2\) \(12.457\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q-iq^{3}+(1+2i)q^{5}+iq^{7}-q^{9}+3q^{11}+\cdots\)
1560.2.l.c \(6\) \(12.457\) 6.0.5161984.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{3}-\beta _{5}q^{5}-q^{9}+(-2+\beta _{4}+\cdots)q^{11}+\cdots\)
1560.2.l.d \(8\) \(12.457\) 8.0.\(\cdots\).2 None \(0\) \(0\) \(-2\) \(0\) \(q-\beta _{2}q^{3}-\beta _{7}q^{5}+(-\beta _{1}+2\beta _{2})q^{7}+\cdots\)
1560.2.l.e \(8\) \(12.457\) 8.0.1698758656.6 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{3}+(-\beta _{2}-\beta _{3})q^{5}-\beta _{4}q^{7}+\cdots\)
1560.2.l.f \(10\) \(12.457\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(0\) \(2\) \(0\) \(q+\beta _{6}q^{3}+\beta _{2}q^{5}-\beta _{9}q^{7}-q^{9}+(1+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1560, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1560, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(260, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(390, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(520, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(780, [\chi])\)\(^{\oplus 2}\)