Properties

Label 20.7.b
Level $20$
Weight $7$
Character orbit 20.b
Rep. character $\chi_{20}(11,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $1$
Sturm bound $21$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 20 = 2^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 20.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(21\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(20, [\chi])\).

Total New Old
Modular forms 20 12 8
Cusp forms 16 12 4
Eisenstein series 4 0 4

Trace form

\( 12q - 10q^{2} + 156q^{4} - 672q^{6} + 440q^{8} - 1996q^{9} + O(q^{10}) \) \( 12q - 10q^{2} + 156q^{4} - 672q^{6} + 440q^{8} - 1996q^{9} + 750q^{10} - 440q^{12} - 5040q^{13} + 6248q^{14} + 3312q^{16} + 6840q^{17} + 15790q^{18} - 3500q^{20} - 27464q^{21} - 26160q^{22} + 28528q^{24} + 37500q^{25} - 18684q^{26} + 19320q^{28} - 74968q^{29} - 13000q^{30} - 60800q^{32} + 112880q^{33} + 48204q^{34} - 128580q^{36} + 62640q^{37} + 74800q^{38} + 57000q^{40} - 16976q^{41} - 138360q^{42} - 222160q^{44} + 77000q^{45} - 144792q^{46} + 297600q^{48} + 72564q^{49} - 31250q^{50} + 548280q^{52} + 322160q^{53} + 150416q^{54} - 246512q^{56} - 1213440q^{57} + 350700q^{58} + 157000q^{60} + 46464q^{61} - 7120q^{62} - 542784q^{64} - 133000q^{65} - 65200q^{66} - 1678280q^{68} + 41256q^{69} - 360000q^{70} + 2317560q^{72} - 415080q^{73} + 1581924q^{74} + 208320q^{76} + 75600q^{77} + 473200q^{78} + 734000q^{80} + 2287428q^{81} - 3169500q^{82} - 2256224q^{84} + 372000q^{85} - 62512q^{86} - 278880q^{88} + 278392q^{89} - 2162250q^{90} + 4095720q^{92} - 3646000q^{93} + 4706568q^{94} - 2641152q^{96} + 2344680q^{97} + 1050270q^{98} + O(q^{100}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(20, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
20.7.b.a \(12\) \(4.601\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-10\) \(0\) \(0\) \(0\) \(q+(-1-\beta _{2})q^{2}+(-\beta _{2}-\beta _{6})q^{3}+(13+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{7}^{\mathrm{old}}(20, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(20, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(4, [\chi])\)\(^{\oplus 2}\)