Properties

Label 50.26.b
Level $50$
Weight $26$
Character orbit 50.b
Rep. character $\chi_{50}(49,\cdot)$
Character field $\Q$
Dimension $38$
Newform subspaces $8$
Sturm bound $195$
Trace bound $6$

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Defining parameters

Level: \( N \) \(=\) \( 50 = 2 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 26 \)
Character orbit: \([\chi]\) \(=\) 50.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(195\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{26}(50, [\chi])\).

Total New Old
Modular forms 194 38 156
Cusp forms 182 38 144
Eisenstein series 12 0 12

Trace form

\( 38 q - 637534208 q^{4} + 8776835072 q^{6} - 12991242549664 q^{9} - 30472316016774 q^{11} - 330406594985984 q^{14} + 10\!\cdots\!28 q^{16} + 35\!\cdots\!90 q^{19} + 41\!\cdots\!56 q^{21} - 14\!\cdots\!52 q^{24}+ \cdots + 23\!\cdots\!72 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{26}^{\mathrm{new}}(50, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
50.26.b.a 50.b 5.b $2$ $197.998$ \(\Q(\sqrt{-1}) \) None 2.26.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2048\beta q^{2}+48978\beta q^{3}-16777216 q^{4}+\cdots\)
50.26.b.b 50.b 5.b $2$ $197.998$ \(\Q(\sqrt{-1}) \) None 10.26.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-2048\beta q^{2}+81432\beta q^{3}-16777216 q^{4}+\cdots\)
50.26.b.c 50.b 5.b $4$ $197.998$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None 10.26.a.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2^{11}\beta _{1}q^{2}+(136303\beta _{1}-\beta _{3})q^{3}+\cdots\)
50.26.b.d 50.b 5.b $4$ $197.998$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None 10.26.a.d \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-2^{11}\beta _{1}q^{2}+(-24273\beta _{1}-\beta _{3})q^{3}+\cdots\)
50.26.b.e 50.b 5.b $4$ $197.998$ \(\mathbb{Q}[x]/(x^{4} + \cdots)\) None 2.26.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2^{11}\beta _{1}q^{2}+(-94962\beta _{1}-\beta _{2})q^{3}+\cdots\)
50.26.b.f 50.b 5.b $4$ $197.998$ \(\mathbb{Q}[x]/(x^{4} + \cdots)\) None 10.26.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-2^{11}\beta _{1}q^{2}+(109647\beta _{1}-\beta _{2})q^{3}+\cdots\)
50.26.b.g 50.b 5.b $8$ $197.998$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None 50.26.a.g \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2^{12}\beta _{3}q^{2}+(\beta _{1}-26589\beta _{3})q^{3}+\cdots\)
50.26.b.h 50.b 5.b $10$ $197.998$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None 50.26.a.i \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2^{12}\beta _{5}q^{2}+(-144799\beta _{5}+\beta _{6}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{26}^{\mathrm{old}}(50, [\chi])\) into lower level spaces

\( S_{26}^{\mathrm{old}}(50, [\chi]) \simeq \) \(S_{26}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 2}\)