Properties

Label 48.5.e
Level $48$
Weight $5$
Character orbit 48.e
Rep. character $\chi_{48}(17,\cdot)$
Character field $\Q$
Dimension $7$
Newform subspaces $3$
Sturm bound $40$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 48.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(40\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(48, [\chi])\).

Total New Old
Modular forms 38 9 29
Cusp forms 26 7 19
Eisenstein series 12 2 10

Trace form

\( 7 q + q^{3} + 18 q^{7} + 55 q^{9} + O(q^{10}) \) \( 7 q + q^{3} + 18 q^{7} + 55 q^{9} - 2 q^{13} + 256 q^{15} - 62 q^{19} + 222 q^{21} - 745 q^{25} - 431 q^{27} - 2510 q^{31} + 512 q^{33} - 1122 q^{37} + 3730 q^{39} + 4706 q^{43} + 1024 q^{45} + 1013 q^{49} - 7168 q^{51} - 8704 q^{55} - 338 q^{57} + 3646 q^{61} + 15282 q^{63} + 18178 q^{67} - 1024 q^{69} - 2450 q^{73} - 30607 q^{75} - 26254 q^{79} - 5273 q^{81} - 4096 q^{85} + 31488 q^{87} + 42564 q^{91} - 11330 q^{93} + 12686 q^{97} - 48640 q^{99} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(48, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
48.5.e.a 48.e 3.b $1$ $4.962$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(-9\) \(0\) \(94\) $\mathrm{U}(1)[D_{2}]$ \(q-9q^{3}+94q^{7}+3^{4}q^{9}+146q^{13}+\cdots\)
48.5.e.b 48.e 3.b $2$ $4.962$ \(\Q(\sqrt{-2}) \) None \(0\) \(6\) \(0\) \(-52\) $\mathrm{SU}(2)[C_{2}]$ \(q+(3+\beta )q^{3}+2\beta q^{5}-26q^{7}+(-63+\cdots)q^{9}+\cdots\)
48.5.e.c 48.e 3.b $4$ $4.962$ \(\Q(\sqrt{-2}, \sqrt{13})\) None \(0\) \(4\) \(0\) \(-24\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+\beta _{2})q^{3}+(-\beta _{1}-2\beta _{2}-\beta _{3})q^{5}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(48, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(48, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 2}\)