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Properties

Label 63.10.c
Level $63$
Weight $10$
Character orbit 63.c
Rep. character $\chi_{63}(62,\cdot)$
Character field $\Q$
Dimension $24$
Newform subspaces $2$
Sturm bound $80$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 63.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(80\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(63, [\chi])\).

Total New Old
Modular forms 76 24 52
Cusp forms 68 24 44
Eisenstein series 8 0 8

Trace form

\( 24 q - 6144 q^{4} - 11580 q^{7} + 1459644 q^{16} + 5671548 q^{22} + 14547768 q^{25} + 4670484 q^{28} + 11845824 q^{37} + 5135496 q^{43} - 150971292 q^{46} + 98162808 q^{49} - 880309548 q^{58} + 1180268544 q^{64}+ \cdots + 2258720784 q^{91}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{10}^{\mathrm{new}}(63, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
63.10.c.a 63.c 21.c $4$ $32.447$ \(\Q(\sqrt{-2}, \sqrt{7})\) \(\Q(\sqrt{-7}) \) 63.10.c.a \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(-4\beta _{1}+\beta _{2})q^{2}+(-2^{9}+85\beta _{3})q^{4}+\cdots\)
63.10.c.b 63.c 21.c $20$ $32.447$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None 63.10.c.b \(0\) \(0\) \(0\) \(-11580\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{11}q^{2}+(-205-\beta _{1})q^{4}-\beta _{10}q^{5}+\cdots\)

Decomposition of \(S_{10}^{\mathrm{old}}(63, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(63, [\chi]) \simeq \) \(S_{10}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)