Properties

Label 19.7.b
Level $19$
Weight $7$
Character orbit 19.b
Rep. character $\chi_{19}(18,\cdot)$
Character field $\Q$
Dimension $9$
Newform subspaces $2$
Sturm bound $11$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 19 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 19.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(11\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(19, [\chi])\).

Total New Old
Modular forms 11 11 0
Cusp forms 9 9 0
Eisenstein series 2 2 0

Trace form

\( 9q - 390q^{4} + 54q^{5} - 358q^{6} + 470q^{7} - 323q^{9} + O(q^{10}) \) \( 9q - 390q^{4} + 54q^{5} - 358q^{6} + 470q^{7} - 323q^{9} - 3086q^{11} + 15642q^{16} - 3622q^{17} + 13693q^{19} - 14188q^{20} - 29642q^{23} + 64310q^{24} + 65783q^{25} - 37522q^{26} - 96778q^{28} - 187696q^{30} + 177860q^{35} + 81708q^{36} + 103318q^{38} + 43724q^{39} - 429970q^{42} + 118170q^{43} + 625544q^{44} - 230378q^{45} - 175398q^{47} - 47421q^{49} + 390202q^{54} + 4868q^{55} - 186860q^{57} - 405186q^{58} - 111610q^{61} - 1461908q^{62} + 307282q^{63} - 595914q^{64} + 1539556q^{66} + 627590q^{68} + 864018q^{73} + 2645844q^{74} - 3008264q^{76} - 2403120q^{77} + 2123488q^{80} - 3748207q^{81} + 1847172q^{82} - 647990q^{83} + 2631800q^{85} + 2802652q^{87} + 5224538q^{92} + 1507528q^{93} - 2013502q^{95} - 8462238q^{96} - 245974q^{99} + O(q^{100}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(19, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
19.7.b.a \(1\) \(4.371\) \(\Q\) \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(-54\) \(610\) \(q+2^{6}q^{4}-54q^{5}+610q^{7}+3^{6}q^{9}+\cdots\)
19.7.b.b \(8\) \(4.371\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(108\) \(-140\) \(q+\beta _{1}q^{2}-\beta _{2}q^{3}+(-57+\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots\)