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

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

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

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