Properties

Label 48.9.e
Level $48$
Weight $9$
Character orbit 48.e
Rep. character $\chi_{48}(17,\cdot)$
Character field $\Q$
Dimension $15$
Newform subspaces $5$
Sturm bound $72$
Trace bound $3$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 48.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(72\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(48, [\chi])\).

Total New Old
Modular forms 70 17 53
Cusp forms 58 15 43
Eisenstein series 12 2 10

Trace form

\( 15 q + q^{3} - 1502 q^{7} + 1903 q^{9} + O(q^{10}) \) \( 15 q + q^{3} - 1502 q^{7} + 1903 q^{9} - 2 q^{13} - 91904 q^{15} - 64638 q^{19} + 164286 q^{21} - 1178065 q^{25} - 639071 q^{27} - 622494 q^{31} - 1101568 q^{33} - 2421442 q^{37} + 480802 q^{39} - 5226814 q^{43} - 1189376 q^{45} + 10829293 q^{49} + 6155264 q^{51} - 1769984 q^{55} + 7569502 q^{57} - 8066 q^{61} + 18421602 q^{63} + 33005058 q^{67} + 38090240 q^{69} - 39521570 q^{73} - 2835487 q^{75} + 832226 q^{79} + 19658959 q^{81} - 20658176 q^{85} + 8110848 q^{87} - 119495548 q^{91} - 1008770 q^{93} - 84221154 q^{97} + 12036608 q^{99} + O(q^{100}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(48, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
48.9.e.a 48.e 3.b $1$ $19.554$ \(\Q\) \(\Q(\sqrt{-3}) \) 12.9.c.a \(0\) \(-81\) \(0\) \(-4034\) $\mathrm{U}(1)[D_{2}]$ \(q-3^{4}q^{3}-4034q^{7}+3^{8}q^{9}-35806q^{13}+\cdots\)
48.9.e.b 48.e 3.b $2$ $19.554$ \(\Q(\sqrt{-14}) \) None 3.9.b.a \(0\) \(-90\) \(0\) \(3500\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-45-3\beta )q^{3}+10\beta q^{5}+1750q^{7}+\cdots\)
48.9.e.c 48.e 3.b $2$ $19.554$ \(\Q(\sqrt{-110}) \) None 12.9.c.b \(0\) \(102\) \(0\) \(6188\) $\mathrm{SU}(2)[C_{2}]$ \(q+(51+\beta )q^{3}+18\beta q^{5}+3094q^{7}+\cdots\)
48.9.e.d 48.e 3.b $2$ $19.554$ \(\Q(\sqrt{-2}) \) None 6.9.b.a \(0\) \(126\) \(0\) \(-5572\) $\mathrm{SU}(2)[C_{2}]$ \(q+(63-3\beta )q^{3}+34\beta q^{5}-2786q^{7}+\cdots\)
48.9.e.e 48.e 3.b $8$ $19.554$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 24.9.e.a \(0\) \(-56\) \(0\) \(-1584\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-7-\beta _{2})q^{3}+(-\beta _{2}+\beta _{4})q^{5}+(-198+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{9}^{\mathrm{old}}(48, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(48, [\chi]) \simeq \) \(S_{9}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 2}\)