Properties

Label 12.10.b
Level $12$
Weight $10$
Character orbit 12.b
Rep. character $\chi_{12}(11,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $1$
Sturm bound $20$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 12 = 2^{2} \cdot 3 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 12.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 12 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(20\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(12, [\chi])\).

Total New Old
Modular forms 20 20 0
Cusp forms 16 16 0
Eisenstein series 4 4 0

Trace form

\( 16 q - 344 q^{4} - 1608 q^{6} - 13872 q^{9} + O(q^{10}) \) \( 16 q - 344 q^{4} - 1608 q^{6} - 13872 q^{9} - 15952 q^{10} + 42600 q^{12} - 97312 q^{13} + 164896 q^{16} + 256944 q^{18} + 356448 q^{21} + 322128 q^{22} + 166176 q^{24} - 2743728 q^{25} - 1447056 q^{28} + 3286128 q^{30} + 4715520 q^{33} - 13198144 q^{34} - 6827448 q^{36} + 10997600 q^{37} + 23411264 q^{40} + 23964432 q^{42} - 251904 q^{45} - 41256288 q^{46} - 87722976 q^{48} - 21356624 q^{49} + 132124208 q^{52} + 179732232 q^{54} - 88439904 q^{57} - 271309360 q^{58} - 414400704 q^{60} + 50685152 q^{61} + 742710400 q^{64} + 790585104 q^{66} + 63713280 q^{69} - 1188731232 q^{70} - 1250220480 q^{72} + 23382176 q^{73} + 1645242192 q^{76} + 2079579408 q^{78} + 349756560 q^{81} - 3274996000 q^{82} - 3734920464 q^{84} - 247261184 q^{85} + 4467199680 q^{88} + 5726283888 q^{90} - 262825248 q^{93} - 6146963136 q^{94} - 6944875392 q^{96} + 30926624 q^{97} + O(q^{100}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(12, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
12.10.b.a 12.b 12.b $16$ $6.180$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}-\beta _{4}q^{3}+(-21-\beta _{1})q^{4}+\cdots\)