↑

Properties

Label 1530.2.q
Level $1530$
Weight $2$
Character orbit 1530.q
Rep. character $\chi_{1530}(361,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $60$
Newform subspaces $10$
Sturm bound $648$
Trace bound $11$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1530 = 2 \cdot 3^{2} \cdot 5 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1530.q (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 17 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 10 \)
Sturm bound: \(648\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1530, [\chi])\).

Total New Old
Modular forms 680 60 620
Cusp forms 616 60 556
Eisenstein series 64 0 64

Trace form

\( 60 q - 60 q^{4} + O(q^{10}) \) \( 60 q - 60 q^{4} + 4 q^{11} - 8 q^{13} - 8 q^{14} + 60 q^{16} - 16 q^{17} + 4 q^{22} + 24 q^{23} + 40 q^{31} + 4 q^{34} + 8 q^{35} - 8 q^{37} - 16 q^{38} + 4 q^{41} - 4 q^{44} + 8 q^{46} + 16 q^{47} + 4 q^{50} + 8 q^{52} + 32 q^{55} + 8 q^{56} + 32 q^{58} - 8 q^{61} + 32 q^{62} - 60 q^{64} + 8 q^{65} - 56 q^{67} + 16 q^{68} + 16 q^{71} + 4 q^{73} - 16 q^{74} + 40 q^{79} - 28 q^{82} + 8 q^{85} - 72 q^{86} - 4 q^{88} + 88 q^{89} - 40 q^{91} - 24 q^{92} + 40 q^{95} + 20 q^{97} - 52 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1530, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1530.2.q.a 1530.q 17.c $4$ $12.217$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{4}]$ \(q-\zeta_{8}^{2}q^{2}-q^{4}-\zeta_{8}^{3}q^{5}+(-2-2\zeta_{8}^{2}+\cdots)q^{7}+\cdots\)
1530.2.q.b 1530.q 17.c $4$ $12.217$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{8}^{2}q^{2}-q^{4}+\zeta_{8}^{3}q^{5}+(1+2\zeta_{8}+\cdots)q^{7}+\cdots\)
1530.2.q.c 1530.q 17.c $4$ $12.217$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q-\zeta_{8}^{2}q^{2}-q^{4}-\zeta_{8}^{3}q^{5}+(1+2\zeta_{8}+\cdots)q^{7}+\cdots\)
1530.2.q.d 1530.q 17.c $4$ $12.217$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q-\zeta_{8}^{2}q^{2}-q^{4}-\zeta_{8}^{3}q^{5}+(1+2\zeta_{8}+\cdots)q^{7}+\cdots\)
1530.2.q.e 1530.q 17.c $4$ $12.217$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{4}]$ \(q-\zeta_{8}^{2}q^{2}-q^{4}+\zeta_{8}q^{5}+(2-2\zeta_{8}^{2}+\cdots)q^{7}+\cdots\)
1530.2.q.f 1530.q 17.c $8$ $12.217$ 8.0.110166016.2 None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{5}q^{2}-q^{4}+\beta _{2}q^{5}+(\beta _{1}-\beta _{2}+\beta _{5}+\cdots)q^{7}+\cdots\)
1530.2.q.g 1530.q 17.c $8$ $12.217$ 8.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{2}q^{2}-q^{4}-\beta _{4}q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
1530.2.q.h 1530.q 17.c $8$ $12.217$ 8.0.110166016.2 None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{5}q^{2}-q^{4}-\beta _{2}q^{5}+(\beta _{1}-\beta _{2}+\beta _{5}+\cdots)q^{7}+\cdots\)
1530.2.q.i 1530.q 17.c $8$ $12.217$ \(\Q(\zeta_{16})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{16}^{3}q^{2}-q^{4}-\zeta_{16}^{4}q^{5}+\zeta_{16}^{7}q^{7}+\cdots\)
1530.2.q.j 1530.q 17.c $8$ $12.217$ 8.0.18939904.2 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{4}q^{2}-q^{4}-\beta _{3}q^{5}+(-\beta _{2}-\beta _{6}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1530, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1530, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(51, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(102, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(153, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(306, [\chi])\)\(^{\oplus 2}\)