Properties

Label 1520.2.q
Level $1520$
Weight $2$
Character orbit 1520.q
Rep. character $\chi_{1520}(881,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $80$
Newform subspaces $16$
Sturm bound $480$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 1520 = 2^{4} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1520.q (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 16 \)
Sturm bound: \(480\)
Trace bound: \(7\)
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 504 80 424
Cusp forms 456 80 376
Eisenstein series 48 0 48

Trace form

\( 80 q - 4 q^{3} - 8 q^{7} - 44 q^{9} + O(q^{10}) \) \( 80 q - 4 q^{3} - 8 q^{7} - 44 q^{9} + 4 q^{15} + 8 q^{17} + 12 q^{19} - 40 q^{25} + 32 q^{27} - 24 q^{31} - 12 q^{33} - 8 q^{39} + 16 q^{43} + 72 q^{49} - 4 q^{51} - 8 q^{53} - 8 q^{57} - 24 q^{61} + 16 q^{63} - 16 q^{65} - 8 q^{67} + 32 q^{69} + 12 q^{71} - 4 q^{73} + 8 q^{75} + 16 q^{77} + 12 q^{79} - 48 q^{81} + 48 q^{83} + 8 q^{85} - 4 q^{89} + 8 q^{91} - 36 q^{97} + 16 q^{99} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1520.2.q.a 1520.q 19.c $2$ $12.137$ \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(-1\) \(-8\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{5}-4q^{7}+\cdots\)
1520.2.q.b 1520.q 19.c $2$ $12.137$ \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}-\zeta_{6}q^{9}+\cdots\)
1520.2.q.c 1520.q 19.c $2$ $12.137$ \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(1\) \(8\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}+4q^{7}+\cdots\)
1520.2.q.d 1520.q 19.c $2$ $12.137$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(-1\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{5}+2q^{7}+\cdots\)
1520.2.q.e 1520.q 19.c $2$ $12.137$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(1\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}-2q^{7}+\cdots\)
1520.2.q.f 1520.q 19.c $2$ $12.137$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(1\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{5}-q^{7}+3\zeta_{6}q^{9}-5q^{11}+\cdots\)
1520.2.q.g 1520.q 19.c $2$ $12.137$ \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(1\) \(8\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}+4q^{7}+\cdots\)
1520.2.q.h 1520.q 19.c $4$ $12.137$ \(\Q(\sqrt{-3}, \sqrt{17})\) None \(0\) \(-1\) \(-2\) \(-10\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{3}-\beta _{2}q^{5}+(-3-\beta _{3})q^{7}+(-1+\cdots)q^{9}+\cdots\)
1520.2.q.i 1520.q 19.c $6$ $12.137$ 6.0.1783323.2 None \(0\) \(-1\) \(3\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{3}+\beta _{5})q^{3}+(1+\beta _{4})q^{5}+(-1+\cdots)q^{7}+\cdots\)
1520.2.q.j 1520.q 19.c $6$ $12.137$ 6.0.3518667.1 None \(0\) \(1\) \(3\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{3}-\beta _{3}q^{5}+(-1+\beta _{2})q^{7}+(-2+\cdots)q^{9}+\cdots\)
1520.2.q.k 1520.q 19.c $8$ $12.137$ 8.0.4601315889.1 None \(0\) \(-1\) \(-4\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{7}q^{3}-\beta _{5}q^{5}+(\beta _{2}+\beta _{3}+\beta _{4}-\beta _{6}+\cdots)q^{7}+\cdots\)
1520.2.q.l 1520.q 19.c $8$ $12.137$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(4\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{1}+\beta _{4})q^{3}+\beta _{5}q^{5}+(1+\beta _{4}-2\beta _{7})q^{7}+\cdots\)
1520.2.q.m 1520.q 19.c $8$ $12.137$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(1\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{3}+\beta _{4}q^{5}-\beta _{7}q^{7}+(-1+\beta _{1}+\cdots)q^{9}+\cdots\)
1520.2.q.n 1520.q 19.c $8$ $12.137$ 8.0.\(\cdots\).1 None \(0\) \(1\) \(-4\) \(6\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{3}-\beta _{4}q^{5}+(1-\beta _{3})q^{7}+(-4+\cdots)q^{9}+\cdots\)
1520.2.q.o 1520.q 19.c $8$ $12.137$ 8.0.4601315889.1 None \(0\) \(3\) \(-4\) \(8\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}+\beta _{5})q^{3}-\beta _{5}q^{5}+(1-\beta _{2}+\cdots)q^{7}+\cdots\)
1520.2.q.p 1520.q 19.c $10$ $12.137$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(-1\) \(5\) \(-10\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{3}+(1-\beta _{6})q^{5}+(-1-\beta _{5})q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1520, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(304, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(380, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(760, [\chi])\)\(^{\oplus 2}\)