Properties

Label 55.4.b
Level $55$
Weight $4$
Character orbit 55.b
Rep. character $\chi_{55}(34,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $2$
Sturm bound $24$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 55 = 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 55.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(24\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(55, [\chi])\).

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

Trace form

\( 16q - 60q^{4} + 10q^{5} + 4q^{6} - 176q^{9} + O(q^{10}) \) \( 16q - 60q^{4} + 10q^{5} + 4q^{6} - 176q^{9} + 62q^{10} + 44q^{11} - 16q^{14} - 26q^{15} + 360q^{16} + 168q^{19} - 116q^{20} - 176q^{21} - 200q^{24} - 126q^{25} + 36q^{26} + 552q^{29} - 950q^{30} + 728q^{31} + 72q^{34} + 252q^{35} + 912q^{36} + 944q^{39} - 1644q^{40} - 408q^{41} - 748q^{44} - 220q^{45} + 876q^{46} - 1484q^{49} - 214q^{50} + 72q^{51} - 2292q^{54} + 198q^{55} + 2496q^{56} - 276q^{59} + 1804q^{60} - 560q^{61} - 1900q^{64} + 1864q^{65} + 528q^{66} - 3196q^{69} - 2152q^{70} - 768q^{71} + 5108q^{74} + 1614q^{75} + 1832q^{76} + 1240q^{79} + 2384q^{80} - 200q^{81} + 5160q^{84} - 684q^{85} - 4396q^{86} - 2104q^{89} - 3064q^{90} + 3384q^{91} + 2200q^{94} - 4584q^{95} - 9208q^{96} - 1408q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(55, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
55.4.b.a \(6\) \(3.245\) \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(0\) \(0\) \(-4\) \(0\) \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{5})q^{3}+(1+\beta _{3})q^{4}+\cdots\)
55.4.b.b \(10\) \(3.245\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(0\) \(14\) \(0\) \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(-6+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots\)