Properties

Label 112.2.v
Level 112
Weight 2
Character orbit 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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
112.2.v.a \(56\) \(0.894\) None \(-2\) \(-6\) \(-6\) \(-8\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database