Properties

Label 637.2.u
Level $637$
Weight $2$
Character orbit 637.u
Rep. character $\chi_{637}(30,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $86$
Newform subspaces $10$
Sturm bound $130$
Trace bound $5$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.u (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 10 \)
Sturm bound: \(130\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(637, [\chi])\).

Total New Old
Modular forms 146 102 44
Cusp forms 114 86 28
Eisenstein series 32 16 16

Trace form

\( 86 q + 3 q^{2} - 4 q^{3} + 39 q^{4} + 6 q^{6} + 82 q^{9} + O(q^{10}) \) \( 86 q + 3 q^{2} - 4 q^{3} + 39 q^{4} + 6 q^{6} + 82 q^{9} + 18 q^{10} + 2 q^{12} + 4 q^{13} - 15 q^{15} - 29 q^{16} - 11 q^{17} - 51 q^{18} + 6 q^{20} - 5 q^{23} + 35 q^{25} + 12 q^{26} - 22 q^{27} - 2 q^{29} - 52 q^{30} + 15 q^{31} - 9 q^{32} + 37 q^{36} + 27 q^{37} - 16 q^{38} + 27 q^{39} + 4 q^{40} + 15 q^{41} - 22 q^{43} + 48 q^{44} + 3 q^{45} + 42 q^{46} - 14 q^{48} + 30 q^{50} - 36 q^{51} - 52 q^{52} + 17 q^{53} + 9 q^{54} + 24 q^{55} - 21 q^{59} - 129 q^{60} - 4 q^{61} - 38 q^{62} - 16 q^{64} - 22 q^{65} + 43 q^{66} + 5 q^{68} - 7 q^{69} - 75 q^{71} + 57 q^{73} + 3 q^{74} - 3 q^{75} + 42 q^{76} - 123 q^{78} + 6 q^{79} + 46 q^{81} - 8 q^{82} - 9 q^{85} - 114 q^{86} - 13 q^{87} - 58 q^{88} - 36 q^{89} + 12 q^{90} + 62 q^{92} + 54 q^{93} - 28 q^{94} + 35 q^{95} + 12 q^{96} + 12 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(637, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
637.2.u.a 637.u 91.u $2$ $5.086$ \(\Q(\sqrt{-3}) \) None 91.2.k.a \(-3\) \(2\) \(3\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-2+\zeta_{6})q^{2}+q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
637.2.u.b 637.u 91.u $2$ $5.086$ \(\Q(\sqrt{-3}) \) None 13.2.e.a \(3\) \(-4\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(2-\zeta_{6})q^{2}-2q^{3}+(1-\zeta_{6})q^{4}+(-1+\cdots)q^{5}+\cdots\)
637.2.u.c 637.u 91.u $2$ $5.086$ \(\Q(\sqrt{-3}) \) None 13.2.e.a \(3\) \(4\) \(3\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(2-\zeta_{6})q^{2}+2q^{3}+(1-\zeta_{6})q^{4}+(1+\cdots)q^{5}+\cdots\)
637.2.u.d 637.u 91.u $4$ $5.086$ \(\Q(\sqrt{-3}, \sqrt{-7})\) None 637.2.q.e \(-3\) \(-2\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1+\beta _{3})q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots\)
637.2.u.e 637.u 91.u $4$ $5.086$ \(\Q(\sqrt{-3}, \sqrt{-7})\) None 637.2.q.e \(-3\) \(2\) \(3\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1+\beta _{3})q^{2}+(\beta _{1}+\beta _{3})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots\)
637.2.u.f 637.u 91.u $4$ $5.086$ \(\Q(\sqrt{-3}, \sqrt{-13})\) None 637.2.q.d \(6\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(2-\beta _{2})q^{2}+(1-\beta _{2})q^{4}+\beta _{1}q^{5}+\cdots\)
637.2.u.g 637.u 91.u $12$ $5.086$ 12.0.\(\cdots\).1 None 91.2.k.b \(0\) \(-6\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{10}q^{2}+(-1+\beta _{1}-\beta _{3}-\beta _{8})q^{3}+\cdots\)
637.2.u.h 637.u 91.u $12$ $5.086$ 12.0.\(\cdots\).1 None 91.2.q.a \(0\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{8}q^{2}+(-\beta _{2}-\beta _{4})q^{3}+(1-\beta _{2}+\cdots)q^{4}+\cdots\)
637.2.u.i 637.u 91.u $12$ $5.086$ 12.0.\(\cdots\).1 None 91.2.q.a \(0\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{8}q^{2}+(-\beta _{2}+\beta _{4})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots\)
637.2.u.j 637.u 91.u $32$ $5.086$ None 637.2.q.j \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(637, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(637, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 2}\)