Properties

Label 6.7.b
Level 6
Weight 7
Character orbit b
Rep. character \(\chi_{6}(5,\cdot)\)
Character field \(\Q\)
Dimension 2
Newforms 1
Sturm bound 7
Trace bound 0

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Defining parameters

Level: \( N \) = \( 6 = 2 \cdot 3 \)
Weight: \( k \) = \( 7 \)
Character orbit: \([\chi]\) = 6.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 3 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(7\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(6, [\chi])\).

Total New Old
Modular forms 8 2 6
Cusp forms 4 2 2
Eisenstein series 4 0 4

Trace form

\( 2q + 42q^{3} - 64q^{4} - 192q^{6} + 4q^{7} + 306q^{9} + O(q^{10}) \) \( 2q + 42q^{3} - 64q^{4} - 192q^{6} + 4q^{7} + 306q^{9} + 1920q^{10} - 1344q^{12} - 5900q^{13} + 5760q^{15} + 2048q^{16} - 8064q^{18} + 10516q^{19} + 84q^{21} + 384q^{22} + 6144q^{24} - 26350q^{25} - 17766q^{27} - 128q^{28} + 40320q^{30} + 45796q^{31} + 1152q^{33} - 50688q^{34} - 9792q^{36} + 68116q^{37} - 123900q^{39} - 61440q^{40} - 384q^{42} - 12812q^{43} + 241920q^{45} + 115968q^{46} + 43008q^{48} - 235290q^{49} - 152064q^{51} + 188800q^{52} - 198720q^{54} - 11520q^{55} + 220836q^{57} - 24960q^{58} - 184320q^{60} - 125132q^{61} + 612q^{63} - 65536q^{64} + 8064q^{66} + 877396q^{67} + 347904q^{69} + 3840q^{70} + 258048q^{72} - 1461020q^{73} - 553350q^{75} - 336512q^{76} + 566400q^{78} + 681124q^{79} - 969246q^{81} + 189696q^{82} - 2688q^{84} + 1520640q^{85} - 74880q^{87} - 12288q^{88} + 293760q^{90} - 11800q^{91} + 961716q^{93} - 2035200q^{94} - 196608q^{96} - 562172q^{97} + 48384q^{99} + O(q^{100}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(6, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
6.7.b.a \(2\) \(1.380\) \(\Q(\sqrt{-2}) \) None \(0\) \(42\) \(0\) \(4\) \(q+\beta q^{2}+(21+3\beta )q^{3}-2^{5}q^{4}-30\beta q^{5}+\cdots\)

Decomposition of \(S_{7}^{\mathrm{old}}(6, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(6, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 2}\)