Properties

Label 50.18.b
Level $50$
Weight $18$
Character orbit 50.b
Rep. character $\chi_{50}(49,\cdot)$
Character field $\Q$
Dimension $26$
Newform subspaces $7$
Sturm bound $135$
Trace bound $6$

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Defining parameters

Level: \( N \) \(=\) \( 50 = 2 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 18 \)
Character orbit: \([\chi]\) \(=\) 50.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(135\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{18}(50, [\chi])\).

Total New Old
Modular forms 134 26 108
Cusp forms 122 26 96
Eisenstein series 12 0 12

Trace form

\( 26 q - 1703936 q^{4} - 1409536 q^{6} - 1153480348 q^{9} - 240451878 q^{11} - 22617832448 q^{14} + 111669149696 q^{16} + 175209015830 q^{19} - 25960786348 q^{21} + 92375351296 q^{24} + 1238593931264 q^{26}+ \cdots + 39\!\cdots\!44 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{18}^{\mathrm{new}}(50, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
50.18.b.a 50.b 5.b $2$ $91.611$ \(\Q(\sqrt{-1}) \) None 10.18.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+128\beta q^{2}+7488\beta q^{3}-65536 q^{4}+\cdots\)
50.18.b.b 50.b 5.b $2$ $91.611$ \(\Q(\sqrt{-1}) \) None 2.18.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-128\beta q^{2}+3042\beta q^{3}-65536 q^{4}+\cdots\)
50.18.b.c 50.b 5.b $4$ $91.611$ \(\mathbb{Q}[x]/(x^{4} + \cdots)\) None 50.18.a.d \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-2^{8}\beta _{1}q^{2}+(-5796\beta _{1}-\beta _{2})q^{3}+\cdots\)
50.18.b.d 50.b 5.b $4$ $91.611$ \(\mathbb{Q}[x]/(x^{4} + \cdots)\) None 10.18.a.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2^{7}\beta _{1}q^{2}+(-327\beta _{1}+\beta _{2})q^{3}-2^{16}q^{4}+\cdots\)
50.18.b.e 50.b 5.b $4$ $91.611$ \(\mathbb{Q}[x]/(x^{4} + \cdots)\) None 10.18.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-2^{7}\beta _{1}q^{2}+(1577\beta _{1}-\beta _{2})q^{3}-2^{16}q^{4}+\cdots\)
50.18.b.f 50.b 5.b $4$ $91.611$ \(\Q(i, \sqrt{2941})\) None 10.18.a.d \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-2^{7}\beta _{1}q^{2}+(4407\beta _{1}+\beta _{2})q^{3}-2^{16}q^{4}+\cdots\)
50.18.b.g 50.b 5.b $6$ $91.611$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None 50.18.a.h \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-2^{8}\beta _{1}q^{2}+(-2504\beta _{1}-\beta _{3})q^{3}+\cdots\)

Decomposition of \(S_{18}^{\mathrm{old}}(50, [\chi])\) into lower level spaces

\( S_{18}^{\mathrm{old}}(50, [\chi]) \simeq \) \(S_{18}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 2}\)