Properties

Label 637.2.c
Level $637$
Weight $2$
Character orbit 637.c
Rep. character $\chi_{637}(246,\cdot)$
Character field $\Q$
Dimension $44$
Newform subspaces $7$
Sturm bound $130$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(130\)
Trace bound: \(3\)
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 72 54 18
Cusp forms 56 44 12
Eisenstein series 16 10 6

Trace form

\( 44q - 40q^{4} + 36q^{9} + O(q^{10}) \) \( 44q - 40q^{4} + 36q^{9} + 20q^{12} - 8q^{13} + 24q^{16} + 8q^{17} - 36q^{22} - 16q^{23} - 36q^{25} - 12q^{26} + 12q^{27} + 8q^{29} - 44q^{30} - 20q^{36} + 4q^{38} + 4q^{39} + 20q^{40} - 24q^{43} - 8q^{48} - 48q^{51} + 20q^{52} + 40q^{53} - 12q^{55} - 28q^{61} - 16q^{62} - 36q^{64} + 16q^{65} - 28q^{66} - 20q^{68} + 4q^{69} + 36q^{74} - 44q^{75} + 12q^{78} + 16q^{79} + 12q^{81} + 56q^{82} + 40q^{87} + 88q^{88} + 12q^{90} + 28q^{92} - 20q^{94} - 8q^{95} + O(q^{100}) \)

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.c.a \(2\) \(5.086\) \(\Q(\sqrt{-1}) \) None \(0\) \(-4\) \(0\) \(0\) \(q+2iq^{2}-2q^{3}-2q^{4}+iq^{5}-4iq^{6}+\cdots\)
637.2.c.b \(2\) \(5.086\) \(\Q(\sqrt{-13}) \) \(\Q(\sqrt{-91}) \) \(0\) \(0\) \(0\) \(0\) \(q+2q^{4}+\beta q^{5}-3q^{9}+\beta q^{13}+4q^{16}+\cdots\)
637.2.c.c \(2\) \(5.086\) \(\Q(\sqrt{-1}) \) None \(0\) \(4\) \(0\) \(0\) \(q+2iq^{2}+2q^{3}-2q^{4}-iq^{5}+4iq^{6}+\cdots\)
637.2.c.d \(6\) \(5.086\) 6.0.350464.1 None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{3}+\beta _{4})q^{2}-\beta _{1}q^{3}+(-1-\beta _{1}+\cdots)q^{4}+\cdots\)
637.2.c.e \(8\) \(5.086\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(-4\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-1-\beta _{4})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
637.2.c.f \(8\) \(5.086\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(4\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(1+\beta _{4})q^{3}+(-1+\beta _{2})q^{4}+\cdots\)
637.2.c.g \(16\) \(5.086\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{10}q^{2}-\beta _{11}q^{3}+(-1+\beta _{2})q^{4}+\cdots\)

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

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