Properties

Label 184.2.b
Level $184$
Weight $2$
Character orbit 184.b
Rep. character $\chi_{184}(93,\cdot)$
Character field $\Q$
Dimension $22$
Newform subspaces $3$
Sturm bound $48$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 184 = 2^{3} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 184.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(48\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(184, [\chi])\).

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

Trace form

\( 22q + 3q^{6} + 3q^{8} - 22q^{9} + O(q^{10}) \) \( 22q + 3q^{6} + 3q^{8} - 22q^{9} - 2q^{10} + q^{12} - 8q^{14} - 16q^{16} - 4q^{17} - 7q^{18} + 16q^{20} + 20q^{22} - 6q^{23} - 18q^{25} + 5q^{26} + 6q^{28} + 26q^{30} + 12q^{31} + 8q^{33} - 10q^{34} + 7q^{36} + 12q^{38} - 4q^{39} - 22q^{40} - 4q^{41} - 44q^{42} + 18q^{44} - 4q^{47} - 39q^{48} + 6q^{49} - 28q^{50} + q^{52} + 15q^{54} + 16q^{55} - 22q^{56} + 8q^{57} - 15q^{58} + 56q^{60} - 29q^{62} - 40q^{63} + 3q^{64} + 16q^{65} + 34q^{66} - 32q^{68} + 16q^{70} + 4q^{71} - 33q^{72} - 4q^{73} - 10q^{74} - 28q^{76} + 57q^{78} + 22q^{80} + 30q^{81} - 9q^{82} + 18q^{84} - 22q^{86} + 20q^{87} + 60q^{88} - 20q^{89} + 16q^{90} - 39q^{94} + 56q^{95} + 41q^{96} - 4q^{97} - 32q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(184, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
184.2.b.a \(2\) \(1.469\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(-8\) \(q+\beta q^{2}-2\beta q^{3}-2q^{4}-\beta q^{5}+4q^{6}+\cdots\)
184.2.b.b \(8\) \(1.469\) 8.0.5198736512.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{5}q^{2}-\beta _{4}q^{3}+\beta _{1}q^{4}-\beta _{6}q^{5}+\cdots\)
184.2.b.c \(12\) \(1.469\) 12.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(8\) \(q-\beta _{1}q^{2}-\beta _{7}q^{3}+\beta _{2}q^{4}+(-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)