Properties

Label 1638.2.j
Level $1638$
Weight $2$
Character orbit 1638.j
Rep. character $\chi_{1638}(235,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $80$
Newform subspaces $20$
Sturm bound $672$
Trace bound $7$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1638.j (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 20 \)
Sturm bound: \(672\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(11\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1638, [\chi])\).

Total New Old
Modular forms 704 80 624
Cusp forms 640 80 560
Eisenstein series 64 0 64

Trace form

\( 80 q - 40 q^{4} - 8 q^{5} + O(q^{10}) \) \( 80 q - 40 q^{4} - 8 q^{5} + 4 q^{10} - 4 q^{11} - 4 q^{13} + 10 q^{14} - 40 q^{16} + 18 q^{17} + 4 q^{19} + 16 q^{20} + 12 q^{22} + 12 q^{23} - 44 q^{25} - 6 q^{26} - 12 q^{28} + 4 q^{29} - 4 q^{31} - 32 q^{34} + 12 q^{35} - 10 q^{38} + 4 q^{40} - 32 q^{41} + 16 q^{43} - 4 q^{44} - 20 q^{46} - 12 q^{47} + 62 q^{49} - 16 q^{50} + 2 q^{52} - 22 q^{53} + 8 q^{55} - 2 q^{56} + 8 q^{59} - 34 q^{61} - 20 q^{62} + 80 q^{64} + 4 q^{65} - 8 q^{67} + 18 q^{68} + 8 q^{71} - 4 q^{73} - 8 q^{76} - 24 q^{77} - 8 q^{80} - 24 q^{82} + 24 q^{83} + 64 q^{85} + 12 q^{86} - 6 q^{88} - 12 q^{89} + 16 q^{91} - 24 q^{92} + 22 q^{94} + 8 q^{95} - 16 q^{97} + 72 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1638, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1638.2.j.a 1638.j 7.c $2$ $13.079$ \(\Q(\sqrt{-3}) \) None 546.2.i.e \(-1\) \(0\) \(-2\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-2\zeta_{6}q^{5}+\cdots\)
1638.2.j.b 1638.j 7.c $2$ $13.079$ \(\Q(\sqrt{-3}) \) None 546.2.i.g \(-1\) \(0\) \(-2\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-2\zeta_{6}q^{5}+\cdots\)
1638.2.j.c 1638.j 7.c $2$ $13.079$ \(\Q(\sqrt{-3}) \) None 182.2.f.a \(-1\) \(0\) \(0\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+(2+\zeta_{6})q^{7}+\cdots\)
1638.2.j.d 1638.j 7.c $2$ $13.079$ \(\Q(\sqrt{-3}) \) None 1638.2.j.d \(-1\) \(0\) \(1\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+\zeta_{6}q^{5}+(-3+\cdots)q^{7}+\cdots\)
1638.2.j.e 1638.j 7.c $2$ $13.079$ \(\Q(\sqrt{-3}) \) None 546.2.i.f \(-1\) \(0\) \(1\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots\)
1638.2.j.f 1638.j 7.c $2$ $13.079$ \(\Q(\sqrt{-3}) \) None 546.2.i.c \(1\) \(0\) \(-4\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-4\zeta_{6}q^{5}+\cdots\)
1638.2.j.g 1638.j 7.c $2$ $13.079$ \(\Q(\sqrt{-3}) \) None 1638.2.j.d \(1\) \(0\) \(-1\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(-3+\cdots)q^{7}+\cdots\)
1638.2.j.h 1638.j 7.c $2$ $13.079$ \(\Q(\sqrt{-3}) \) None 546.2.i.b \(1\) \(0\) \(-1\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots\)
1638.2.j.i 1638.j 7.c $2$ $13.079$ \(\Q(\sqrt{-3}) \) None 546.2.i.d \(1\) \(0\) \(0\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+(-2-\zeta_{6})q^{7}+\cdots\)
1638.2.j.j 1638.j 7.c $2$ $13.079$ \(\Q(\sqrt{-3}) \) None 546.2.i.a \(1\) \(0\) \(3\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+3\zeta_{6}q^{5}+\cdots\)
1638.2.j.k 1638.j 7.c $4$ $13.079$ \(\Q(\sqrt{-3}, \sqrt{7})\) None 546.2.i.j \(-2\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\beta _{2})q^{2}+\beta _{2}q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
1638.2.j.l 1638.j 7.c $4$ $13.079$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None 1638.2.j.l \(-2\) \(0\) \(0\) \(10\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{2}+(-1+\beta _{1})q^{4}-\beta _{2}q^{5}+(2+\cdots)q^{7}+\cdots\)
1638.2.j.m 1638.j 7.c $4$ $13.079$ \(\Q(\sqrt{2}, \sqrt{-3})\) None 546.2.i.i \(2\) \(0\) \(-4\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{2}q^{2}+(-1-\beta _{2})q^{4}+(-\beta _{1}+2\beta _{2}+\cdots)q^{5}+\cdots\)
1638.2.j.n 1638.j 7.c $4$ $13.079$ \(\Q(\sqrt{2}, \sqrt{-3})\) None 546.2.i.h \(2\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{2})q^{2}+\beta _{2}q^{4}+\beta _{1}q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)
1638.2.j.o 1638.j 7.c $4$ $13.079$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None 1638.2.j.l \(2\) \(0\) \(0\) \(10\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(-1+\beta _{1})q^{4}-\beta _{2}q^{5}+(2+\cdots)q^{7}+\cdots\)
1638.2.j.p 1638.j 7.c $6$ $13.079$ 6.0.309123.1 None 182.2.f.b \(-3\) \(0\) \(-2\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{4}q^{2}+(-1+\beta _{4})q^{4}+(-\beta _{1}-\beta _{4}+\cdots)q^{5}+\cdots\)
1638.2.j.q 1638.j 7.c $6$ $13.079$ 6.0.21870000.1 None 546.2.i.k \(-3\) \(0\) \(3\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{2}q^{2}+(-1-\beta _{2})q^{4}+(-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
1638.2.j.r 1638.j 7.c $8$ $13.079$ 8.0.8681953329.1 None 182.2.f.c \(4\) \(0\) \(2\) \(7\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{3})q^{2}+\beta _{3}q^{4}+(1+\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots\)
1638.2.j.s 1638.j 7.c $10$ $13.079$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None 1638.2.j.s \(-5\) \(0\) \(1\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\beta _{2})q^{2}+\beta _{2}q^{4}+(\beta _{6}-\beta _{8}+\cdots)q^{5}+\cdots\)
1638.2.j.t 1638.j 7.c $10$ $13.079$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None 1638.2.j.s \(5\) \(0\) \(-1\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{2}q^{2}+(-1-\beta _{2})q^{4}-\beta _{8}q^{5}+(-1+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1638, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1638, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(546, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(819, [\chi])\)\(^{\oplus 2}\)