↑

Properties

Label 624.2.q
Level $624$
Weight $2$
Character orbit 624.q
Rep. character $\chi_{624}(289,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $28$
Newform subspaces $10$
Sturm bound $224$
Trace bound $7$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 624.q (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 10 \)
Sturm bound: \(224\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(624, [\chi])\).

Total New Old
Modular forms 248 28 220
Cusp forms 200 28 172
Eisenstein series 48 0 48

Trace form

\( 28 q - 2 q^{3} + 4 q^{5} + 2 q^{7} - 14 q^{9} + O(q^{10}) \) \( 28 q - 2 q^{3} + 4 q^{5} + 2 q^{7} - 14 q^{9} + 2 q^{13} + 2 q^{17} - 4 q^{19} + 24 q^{25} + 4 q^{27} - 2 q^{29} - 4 q^{31} - 2 q^{37} + 4 q^{39} + 18 q^{41} - 2 q^{43} - 2 q^{45} + 48 q^{47} - 18 q^{49} + 24 q^{51} - 12 q^{53} + 36 q^{55} + 16 q^{57} - 4 q^{59} + 6 q^{61} + 2 q^{63} + 2 q^{65} + 14 q^{67} + 32 q^{71} - 28 q^{73} - 6 q^{75} - 16 q^{77} - 92 q^{79} - 14 q^{81} + 40 q^{83} + 2 q^{85} + 24 q^{87} - 36 q^{89} + 6 q^{91} - 44 q^{95} - 8 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(624, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
624.2.q.a 624.q 13.c $2$ $4.983$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(-4\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}-2q^{5}+\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots\)
624.2.q.b 624.q 13.c $2$ $4.983$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(-2\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}-q^{5}-2\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots\)
624.2.q.c 624.q 13.c $2$ $4.983$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(-2\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}-q^{5}+2\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots\)
624.2.q.d 624.q 13.c $2$ $4.983$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(4\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+2q^{5}+\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots\)
624.2.q.e 624.q 13.c $2$ $4.983$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(6\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+3q^{5}-4\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots\)
624.2.q.f 624.q 13.c $2$ $4.983$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(6\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}+3q^{5}-\zeta_{6}q^{9}+(3+\zeta_{6})q^{13}+\cdots\)
624.2.q.g 624.q 13.c $2$ $4.983$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(6\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}+3q^{5}+2\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots\)
624.2.q.h 624.q 13.c $4$ $4.983$ \(\Q(\sqrt{-3}, \sqrt{17})\) None \(0\) \(2\) \(-6\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{2})q^{3}+(-1+\beta _{3})q^{5}+(\beta _{1}-2\beta _{2}+\cdots)q^{7}+\cdots\)
624.2.q.i 624.q 13.c $4$ $4.983$ \(\Q(\sqrt{-3}, \sqrt{13})\) None \(0\) \(2\) \(-4\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{1})q^{3}-q^{5}+(\beta _{1}+\beta _{2})q^{7}-\beta _{1}q^{9}+\cdots\)
624.2.q.j 624.q 13.c $6$ $4.983$ 6.0.2101707.2 None \(0\) \(-3\) \(0\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{3}q^{3}+\beta _{2}q^{5}+(-1-2\beta _{4}+\beta _{5})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(624, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(624, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(156, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(208, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(312, [\chi])\)\(^{\oplus 2}\)