Properties

Label 100.9.b
Level $100$
Weight $9$
Character orbit 100.b
Rep. character $\chi_{100}(51,\cdot)$
Character field $\Q$
Dimension $73$
Newform subspaces $7$
Sturm bound $135$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 100 = 2^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 100.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(135\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(100, [\chi])\).

Total New Old
Modular forms 126 79 47
Cusp forms 114 73 41
Eisenstein series 12 6 6

Trace form

\( 73 q - 2 q^{2} - 330 q^{4} - 742 q^{6} + 2728 q^{8} - 144623 q^{9} + 14120 q^{12} - 39974 q^{13} + 3892 q^{14} + 192178 q^{16} - 110374 q^{17} + 443558 q^{18} + 35896 q^{21} - 72640 q^{22} - 212978 q^{24}+ \cdots + 269309638 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{9}^{\mathrm{new}}(100, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
100.9.b.a 100.b 4.b $1$ $40.738$ \(\Q\) \(\Q(\sqrt{-1}) \) 4.9.b.a \(-16\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-2^{4}q^{2}+2^{8}q^{4}-2^{12}q^{8}+3^{8}q^{9}+\cdots\)
100.9.b.b 100.b 4.b $2$ $40.738$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-5}) \) 20.9.d.a \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+8\beta q^{2}+79\beta q^{3}-256 q^{4}-2528 q^{6}+\cdots\)
100.9.b.c 100.b 4.b $2$ $40.738$ \(\Q(\sqrt{-39}) \) None 4.9.b.b \(20\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(10-\beta )q^{2}-8\beta q^{3}+(-56-20\beta )q^{4}+\cdots\)
100.9.b.d 100.b 4.b $16$ $40.738$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None 20.9.b.a \(-6\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+(\beta _{1}-\beta _{2})q^{3}+(-3-\beta _{3}+\cdots)q^{4}+\cdots\)
100.9.b.e 100.b 4.b $16$ $40.738$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None 100.9.b.e \(-3\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}-\beta _{1}q^{3}+(-21-\beta _{4})q^{4}+\cdots\)
100.9.b.f 100.b 4.b $16$ $40.738$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None 100.9.b.e \(3\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}-\beta _{1}q^{3}+(-21+\beta _{4})q^{4}+\cdots\)
100.9.b.g 100.b 4.b $20$ $40.738$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None 20.9.d.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{8})q^{3}+(38+\beta _{2}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{9}^{\mathrm{old}}(100, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(100, [\chi]) \simeq \) \(S_{9}^{\mathrm{new}}(4, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 2}\)