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Properties

Label 63.5.d
Level $63$
Weight $5$
Character orbit 63.d
Rep. character $\chi_{63}(55,\cdot)$
Character field $\Q$
Dimension $13$
Newform subspaces $4$
Sturm bound $40$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 63.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(40\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(63, [\chi])\).

Total New Old
Modular forms 36 15 21
Cusp forms 28 13 15
Eisenstein series 8 2 6

Trace form

\( 13 q + 5 q^{2} + 113 q^{4} - 55 q^{7} + 37 q^{8} + O(q^{10}) \) \( 13 q + 5 q^{2} + 113 q^{4} - 55 q^{7} + 37 q^{8} - 46 q^{11} + 461 q^{14} + 1621 q^{16} - 714 q^{22} - 1582 q^{23} - 755 q^{25} - 2699 q^{28} - 1102 q^{29} + 2037 q^{32} + 3624 q^{35} + 3874 q^{37} + 4258 q^{43} - 1254 q^{44} - 15930 q^{46} - 1523 q^{49} - 21739 q^{50} + 8546 q^{53} + 11413 q^{56} - 8730 q^{58} + 47105 q^{64} + 6576 q^{65} - 262 q^{67} - 5376 q^{70} - 37150 q^{71} + 43066 q^{74} + 20402 q^{77} + 15050 q^{79} + 34128 q^{85} - 28406 q^{86} - 75546 q^{88} - 22128 q^{91} - 69558 q^{92} + 30384 q^{95} + 43205 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(63, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
63.5.d.a 63.d 7.b $1$ $6.512$ \(\Q\) \(\Q(\sqrt{-7}) \) \(-1\) \(0\) \(0\) \(49\) $\mathrm{U}(1)[D_{2}]$ \(q-q^{2}-15q^{4}+7^{2}q^{7}+31q^{8}+206q^{11}+\cdots\)
63.5.d.b 63.d 7.b $2$ $6.512$ \(\Q(\sqrt{7}) \) \(\Q(\sqrt{-7}) \) \(0\) \(0\) \(0\) \(-98\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta q^{2}+47q^{4}-7^{2}q^{7}+31\beta q^{8}+\cdots\)
63.5.d.c 63.d 7.b $4$ $6.512$ \(\Q(\sqrt{10}, \sqrt{-106})\) None \(0\) \(0\) \(0\) \(16\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-6q^{4}-\beta _{2}q^{5}+(4+\beta _{3})q^{7}+\cdots\)
63.5.d.d 63.d 7.b $6$ $6.512$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(6\) \(0\) \(0\) \(-22\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1-\beta _{1})q^{2}+(10-\beta _{3})q^{4}-\beta _{4}q^{5}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(63, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(63, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)