Properties

Label 20.9.d
Level $20$
Weight $9$
Character orbit 20.d
Rep. character $\chi_{20}(19,\cdot)$
Character field $\Q$
Dimension $22$
Newform subspaces $3$
Sturm bound $27$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 20 = 2^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 20.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 20 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(27\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(20, [\chi])\).

Total New Old
Modular forms 26 26 0
Cusp forms 22 22 0
Eisenstein series 4 4 0

Trace form

\( 22 q - 240 q^{4} - 170 q^{5} - 1648 q^{6} + 39362 q^{9} + O(q^{10}) \) \( 22 q - 240 q^{4} - 170 q^{5} - 1648 q^{6} + 39362 q^{9} - 4160 q^{10} + 70352 q^{14} + 71872 q^{16} + 315760 q^{20} - 197096 q^{21} - 1451008 q^{24} + 123990 q^{25} - 440448 q^{26} + 701420 q^{29} - 2492080 q^{30} + 4342528 q^{34} + 2231024 q^{36} - 945280 q^{40} - 3769876 q^{41} + 2666880 q^{44} + 4274690 q^{45} + 7319632 q^{46} + 7577602 q^{49} + 3914880 q^{50} - 22762336 q^{54} - 19299328 q^{56} - 22734720 q^{60} - 39783636 q^{61} + 53756160 q^{64} - 44202240 q^{65} + 31902720 q^{66} + 45007384 q^{69} - 8726000 q^{70} + 19114368 q^{74} - 54998400 q^{76} + 89888320 q^{80} + 195550766 q^{81} - 54192896 q^{84} + 68800000 q^{85} + 13805072 q^{86} - 108603220 q^{89} - 230808000 q^{90} + 115025872 q^{94} - 302499328 q^{96} + O(q^{100}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(20, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
20.9.d.a 20.d 20.d $1$ $8.148$ \(\Q\) \(\Q(\sqrt{-5}) \) 20.9.d.a \(-16\) \(158\) \(625\) \(-1922\) $\mathrm{U}(1)[D_{2}]$ \(q-2^{4}q^{2}+158q^{3}+2^{8}q^{4}+5^{4}q^{5}+\cdots\)
20.9.d.b 20.d 20.d $1$ $8.148$ \(\Q\) \(\Q(\sqrt{-5}) \) 20.9.d.a \(16\) \(-158\) \(625\) \(1922\) $\mathrm{U}(1)[D_{2}]$ \(q+2^{4}q^{2}-158q^{3}+2^{8}q^{4}+5^{4}q^{5}+\cdots\)
20.9.d.c 20.d 20.d $20$ $8.148$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None 20.9.d.c \(0\) \(0\) \(-1420\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{6})q^{3}+(-38+\beta _{2}+\cdots)q^{4}+\cdots\)