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 $5$

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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

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

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.u.a \(2\) \(5.086\) \(\Q(\sqrt{-3}) \) None \(-3\) \(2\) \(3\) \(0\) \(q+(-2+\zeta_{6})q^{2}+q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
637.2.u.b \(2\) \(5.086\) \(\Q(\sqrt{-3}) \) None \(3\) \(-4\) \(-3\) \(0\) \(q+(2-\zeta_{6})q^{2}-2q^{3}+(1-\zeta_{6})q^{4}+(-1+\cdots)q^{5}+\cdots\)
637.2.u.c \(2\) \(5.086\) \(\Q(\sqrt{-3}) \) None \(3\) \(4\) \(3\) \(0\) \(q+(2-\zeta_{6})q^{2}+2q^{3}+(1-\zeta_{6})q^{4}+(1+\cdots)q^{5}+\cdots\)
637.2.u.d \(4\) \(5.086\) \(\Q(\sqrt{-3}, \sqrt{-7})\) None \(-3\) \(-2\) \(-3\) \(0\) \(q+(-1+\beta _{3})q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots\)
637.2.u.e \(4\) \(5.086\) \(\Q(\sqrt{-3}, \sqrt{-7})\) None \(-3\) \(2\) \(3\) \(0\) \(q+(-1+\beta _{3})q^{2}+(\beta _{1}+\beta _{3})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots\)
637.2.u.f \(4\) \(5.086\) \(\Q(\sqrt{-3}, \sqrt{-13})\) None \(6\) \(0\) \(0\) \(0\) \(q+(2-\beta _{2})q^{2}+(1-\beta _{2})q^{4}+\beta _{1}q^{5}+\cdots\)
637.2.u.g \(12\) \(5.086\) 12.0.\(\cdots\).1 None \(0\) \(-6\) \(-3\) \(0\) \(q-\beta _{10}q^{2}+(-1+\beta _{1}-\beta _{3}-\beta _{8})q^{3}+\cdots\)
637.2.u.h \(12\) \(5.086\) 12.0.\(\cdots\).1 None \(0\) \(0\) \(-6\) \(0\) \(q+\beta _{8}q^{2}+(-\beta _{2}-\beta _{4})q^{3}+(1-\beta _{2}+\cdots)q^{4}+\cdots\)
637.2.u.i \(12\) \(5.086\) 12.0.\(\cdots\).1 None \(0\) \(0\) \(6\) \(0\) \(q+\beta _{8}q^{2}+(-\beta _{2}+\beta _{4})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots\)
637.2.u.j \(32\) \(5.086\) None \(0\) \(0\) \(0\) \(0\)

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

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