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

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

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
637.2.c.a 637.c 13.b $2$ $5.086$ \(\Q(\sqrt{-1}) \) None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{2}-2q^{3}-2q^{4}+iq^{5}-4iq^{6}+\cdots\)
637.2.c.b 637.c 13.b $2$ $5.086$ \(\Q(\sqrt{-13}) \) \(\Q(\sqrt{-91}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+2q^{4}+\beta q^{5}-3q^{9}+\beta q^{13}+4q^{16}+\cdots\)
637.2.c.c 637.c 13.b $2$ $5.086$ \(\Q(\sqrt{-1}) \) None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{2}+2q^{3}-2q^{4}-iq^{5}+4iq^{6}+\cdots\)
637.2.c.d 637.c 13.b $6$ $5.086$ 6.0.350464.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{3}+\beta _{4})q^{2}-\beta _{1}q^{3}+(-1-\beta _{1}+\cdots)q^{4}+\cdots\)
637.2.c.e 637.c 13.b $8$ $5.086$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-1-\beta _{4})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
637.2.c.f 637.c 13.b $8$ $5.086$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(1+\beta _{4})q^{3}+(-1+\beta _{2})q^{4}+\cdots\)
637.2.c.g 637.c 13.b $16$ $5.086$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{10}q^{2}-\beta _{11}q^{3}+(-1+\beta _{2})q^{4}+\cdots\)

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

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