Properties

Label 112.2.v
Level $112$
Weight $2$
Character orbit 112.v
Rep. character $\chi_{112}(3,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $56$
Newform subspaces $1$
Sturm bound $32$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 112 = 2^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 112.v (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 112 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 1 \)
Sturm bound: \(32\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(112, [\chi])\).

Total New Old
Modular forms 72 72 0
Cusp forms 56 56 0
Eisenstein series 16 16 0

Trace form

\( 56 q - 2 q^{2} - 6 q^{3} - 4 q^{4} - 6 q^{5} - 8 q^{7} + 4 q^{8} + O(q^{10}) \) \( 56 q - 2 q^{2} - 6 q^{3} - 4 q^{4} - 6 q^{5} - 8 q^{7} + 4 q^{8} - 24 q^{10} + 2 q^{11} - 6 q^{12} + 16 q^{14} + 8 q^{16} - 12 q^{17} - 30 q^{18} - 6 q^{19} - 10 q^{21} - 28 q^{22} - 12 q^{23} - 6 q^{24} - 6 q^{26} + 26 q^{28} - 24 q^{29} - 18 q^{30} - 12 q^{32} - 12 q^{33} - 2 q^{35} + 16 q^{36} + 6 q^{37} - 6 q^{38} - 4 q^{39} - 66 q^{40} + 70 q^{42} + 26 q^{44} + 12 q^{45} + 16 q^{46} - 8 q^{49} - 34 q^{51} + 84 q^{52} + 6 q^{53} + 42 q^{54} + 16 q^{56} + 18 q^{58} + 42 q^{59} + 78 q^{60} - 6 q^{61} - 16 q^{64} - 4 q^{65} + 126 q^{66} + 6 q^{67} + 24 q^{68} - 80 q^{70} - 80 q^{71} - 4 q^{72} + 62 q^{74} + 24 q^{75} + 10 q^{77} + 4 q^{78} + 12 q^{80} - 8 q^{81} + 42 q^{82} - 152 q^{84} - 28 q^{85} - 12 q^{87} + 30 q^{88} + 16 q^{91} - 20 q^{92} + 10 q^{93} - 42 q^{94} + 36 q^{96} - 108 q^{98} - 16 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(112, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
112.2.v.a 112.v 112.v $56$ $0.894$ None \(-2\) \(-6\) \(-6\) \(-8\) $\mathrm{SU}(2)[C_{12}]$