Properties

Label 637.2.k
Level $637$
Weight $2$
Character orbit 637.k
Rep. character $\chi_{637}(459,\cdot)$
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.k (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

\( 86q + 2q^{3} - 78q^{4} + 6q^{6} - 41q^{9} + O(q^{10}) \) \( 86q + 2q^{3} - 78q^{4} + 6q^{6} - 41q^{9} - 9q^{10} - 3q^{11} + 2q^{12} + 4q^{13} - 15q^{15} + 58q^{16} + 22q^{17} + 51q^{18} - 6q^{19} + 6q^{20} + 10q^{23} - 18q^{24} + 35q^{25} - 6q^{26} - 22q^{27} - 2q^{29} + 26q^{30} - 15q^{31} + 15q^{33} + 37q^{36} - 16q^{38} - 21q^{39} + 4q^{40} + 15q^{41} - 22q^{43} - 48q^{44} - 14q^{48} + 30q^{50} - 36q^{51} + 5q^{52} + 17q^{53} + 24q^{55} + 111q^{58} + 129q^{60} + 2q^{61} - 38q^{62} - 16q^{64} - 70q^{65} + 43q^{66} - 54q^{67} - 10q^{68} - 7q^{69} - 75q^{71} - 159q^{72} - 57q^{73} - 6q^{74} + 6q^{75} + 42q^{76} - 123q^{78} + 6q^{79} + 78q^{80} - 23q^{81} + 4q^{82} - 9q^{85} + 114q^{86} + 26q^{87} + 29q^{88} + 12q^{90} + 62q^{92} + 14q^{94} - 70q^{95} - 12q^{96} + 12q^{97} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
637.2.k.a \(2\) \(5.086\) \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(-3\) \(0\) \(q+(-1+2\zeta_{6})q^{2}-2\zeta_{6}q^{3}-q^{4}+(-2+\cdots)q^{5}+\cdots\)
637.2.k.b \(2\) \(5.086\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(-3\) \(0\) \(q+(1-2\zeta_{6})q^{2}-\zeta_{6}q^{3}-q^{4}+(-2+\cdots)q^{5}+\cdots\)
637.2.k.c \(2\) \(5.086\) \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(3\) \(0\) \(q+(-1+2\zeta_{6})q^{2}+2\zeta_{6}q^{3}-q^{4}+(2+\cdots)q^{5}+\cdots\)
637.2.k.d \(4\) \(5.086\) \(\Q(\sqrt{-3}, \sqrt{-7})\) None \(0\) \(-1\) \(-3\) \(0\) \(q+(\beta _{1}-\beta _{3})q^{2}+(1-2\beta _{1}-2\beta _{2}+\beta _{3})q^{3}+\cdots\)
637.2.k.e \(4\) \(5.086\) \(\Q(\sqrt{-3}, \sqrt{-13})\) None \(0\) \(0\) \(0\) \(0\) \(q+(1-2\beta _{2})q^{2}-q^{4}+\beta _{1}q^{5}+(1-2\beta _{2}+\cdots)q^{8}+\cdots\)
637.2.k.f \(4\) \(5.086\) \(\Q(\sqrt{-3}, \sqrt{-7})\) None \(0\) \(1\) \(3\) \(0\) \(q+(\beta _{1}-\beta _{3})q^{2}+(-1+2\beta _{1}+2\beta _{2}+\cdots)q^{3}+\cdots\)
637.2.k.g \(12\) \(5.086\) 12.0.\(\cdots\).1 None \(0\) \(0\) \(-6\) \(0\) \(q+(-\beta _{4}+\beta _{8})q^{2}+(\beta _{2}+\beta _{9})q^{3}+(-1+\cdots)q^{4}+\cdots\)
637.2.k.h \(12\) \(5.086\) 12.0.\(\cdots\).1 None \(0\) \(0\) \(6\) \(0\) \(q+(-\beta _{4}+\beta _{8})q^{2}+(-\beta _{2}-\beta _{9})q^{3}+\cdots\)
637.2.k.i \(12\) \(5.086\) 12.0.\(\cdots\).1 None \(0\) \(3\) \(3\) \(0\) \(q+\beta _{9}q^{2}+(-\beta _{1}-\beta _{4}-\beta _{6})q^{3}+(-1+\cdots)q^{4}+\cdots\)
637.2.k.j \(32\) \(5.086\) None \(0\) \(0\) \(0\) \(0\)

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

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