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Properties

Label 4.9.b
Level $4$
Weight $9$
Character orbit 4.b
Rep. character $\chi_{4}(3,\cdot)$
Character field $\Q$
Dimension $3$
Newform subspaces $2$
Sturm bound $4$
Trace bound $1$

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Defining parameters

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

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(4, [\chi])\).

Total New Old
Modular forms 5 5 0
Cusp forms 3 3 0
Eisenstein series 2 2 0

Trace form

\( 3 q - 4 q^{2} + 144 q^{4} + 166 q^{5} - 2496 q^{6} + 11456 q^{8} - 285 q^{9} + O(q^{10}) \) \( 3 q - 4 q^{2} + 144 q^{4} + 166 q^{5} - 2496 q^{6} + 11456 q^{8} - 285 q^{9} - 29064 q^{10} + 49920 q^{12} - 11418 q^{13} - 34944 q^{14} - 52992 q^{16} + 82822 q^{17} + 173436 q^{18} - 338144 q^{20} - 279552 q^{21} + 461760 q^{22} - 359424 q^{24} + 683241 q^{25} + 101752 q^{26} + 698880 q^{28} - 1664282 q^{29} - 1522560 q^{30} + 1534976 q^{32} + 3694080 q^{33} - 2475528 q^{34} + 2062992 q^{36} - 6018138 q^{37} + 486720 q^{38} + 172416 q^{40} + 7871686 q^{41} + 2795520 q^{42} - 9235200 q^{44} - 11091354 q^{45} + 5925504 q^{46} - 5591040 q^{48} + 13380675 q^{49} + 11895156 q^{50} + 490272 q^{52} - 7972058 q^{53} - 7832448 q^{54} - 5031936 q^{56} + 3893760 q^{57} - 19960968 q^{58} + 30451200 q^{60} - 8770074 q^{61} + 1697280 q^{62} + 37392384 q^{64} - 6169588 q^{65} - 36940800 q^{66} - 24405728 q^{68} + 47404032 q^{69} - 21315840 q^{70} + 1680576 q^{72} - 66168378 q^{73} + 84255352 q^{74} - 9734400 q^{76} + 51717120 q^{77} + 13653120 q^{78} - 141377024 q^{80} - 64529469 q^{81} + 14309112 q^{82} + 15654912 q^{84} + 155949132 q^{85} + 148085184 q^{86} + 66493440 q^{88} - 196914362 q^{89} - 68884104 q^{90} - 118510080 q^{92} + 13578240 q^{93} - 190504704 q^{94} + 203833344 q^{96} + 67858182 q^{97} + 16078076 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{9}^{\mathrm{new}}(4, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
4.9.b.a 4.b 4.b $1$ $1.630$ \(\Q\) \(\Q(\sqrt{-1}) \) \(16\) \(0\) \(-1054\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+2^{4}q^{2}+2^{8}q^{4}-1054q^{5}+2^{12}q^{8}+\cdots\)
4.9.b.b 4.b 4.b $2$ $1.630$ \(\Q(\sqrt{-39}) \) None \(-20\) \(0\) \(1220\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-10-\beta )q^{2}-8\beta q^{3}+(-56+20\beta )q^{4}+\cdots\)