Properties

Label 43.7.b
Level $43$
Weight $7$
Character orbit 43.b
Rep. character $\chi_{43}(42,\cdot)$
Character field $\Q$
Dimension $21$
Newform subspaces $2$
Sturm bound $25$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 43.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 43 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(25\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(43, [\chi])\).

Total New Old
Modular forms 23 23 0
Cusp forms 21 21 0
Eisenstein series 2 2 0

Trace form

\( 21q - 732q^{4} - 258q^{6} - 2007q^{9} + O(q^{10}) \) \( 21q - 732q^{4} - 258q^{6} - 2007q^{9} - 1962q^{10} + 978q^{11} - 1906q^{13} - 3876q^{14} + 4048q^{15} + 18996q^{16} + 10402q^{17} + 10544q^{21} - 5570q^{23} + 26966q^{24} - 42279q^{25} - 30802q^{31} - 150472q^{35} - 85454q^{36} + 2266q^{38} + 401286q^{40} - 279294q^{41} - 21347q^{43} - 16288q^{44} + 90806q^{47} + 97005q^{49} + 249476q^{52} + 144358q^{53} + 173740q^{54} + 447864q^{56} - 92904q^{57} + 86502q^{58} - 512398q^{59} + 429848q^{60} + 105252q^{64} - 1246176q^{66} + 626570q^{67} - 2137118q^{68} - 1224106q^{74} + 855716q^{78} - 142114q^{79} + 1002085q^{81} + 673186q^{83} - 637268q^{84} + 3046356q^{86} + 2116740q^{87} - 683716q^{90} - 788974q^{92} - 2711660q^{95} - 2480062q^{96} + 6073314q^{97} + 2550458q^{99} + O(q^{100}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(43, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
43.7.b.a \(1\) \(9.892\) \(\Q\) \(\Q(\sqrt{-43}) \) \(0\) \(0\) \(0\) \(0\) \(q+2^{6}q^{4}+3^{6}q^{9}-1638q^{11}+3706q^{13}+\cdots\)
43.7.b.b \(20\) \(9.892\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(-40+\beta _{2})q^{4}+\cdots\)