Properties

Label 7.6.a
Level 7
Weight 6
Character orbit a
Rep. character \(\chi_{7}(1,\cdot)\)
Character field \(\Q\)
Dimension 3
Newforms 2
Sturm bound 4
Trace bound 1

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Defining parameters

Level: \( N \) = \( 7 \)
Weight: \( k \) = \( 6 \)
Character orbit: \([\chi]\) = 7.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(4\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(7))\).

Total New Old
Modular forms 5 3 2
Cusp forms 3 3 0
Eisenstein series 2 0 2

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators.

\(7\)Dim.
\(+\)\(1\)
\(-\)\(2\)

Trace form

\(3q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 20q^{3} \) \(\mathstrut +\mathstrut 73q^{4} \) \(\mathstrut -\mathstrut 74q^{5} \) \(\mathstrut -\mathstrut 58q^{6} \) \(\mathstrut +\mathstrut 49q^{7} \) \(\mathstrut -\mathstrut 369q^{8} \) \(\mathstrut +\mathstrut 511q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(3q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 20q^{3} \) \(\mathstrut +\mathstrut 73q^{4} \) \(\mathstrut -\mathstrut 74q^{5} \) \(\mathstrut -\mathstrut 58q^{6} \) \(\mathstrut +\mathstrut 49q^{7} \) \(\mathstrut -\mathstrut 369q^{8} \) \(\mathstrut +\mathstrut 511q^{9} \) \(\mathstrut +\mathstrut 764q^{10} \) \(\mathstrut +\mathstrut 628q^{11} \) \(\mathstrut -\mathstrut 2506q^{12} \) \(\mathstrut -\mathstrut 490q^{13} \) \(\mathstrut +\mathstrut 931q^{14} \) \(\mathstrut -\mathstrut 872q^{15} \) \(\mathstrut +\mathstrut 1537q^{16} \) \(\mathstrut +\mathstrut 78q^{17} \) \(\mathstrut +\mathstrut 4007q^{18} \) \(\mathstrut -\mathstrut 3364q^{19} \) \(\mathstrut -\mathstrut 1288q^{20} \) \(\mathstrut +\mathstrut 392q^{21} \) \(\mathstrut -\mathstrut 4072q^{22} \) \(\mathstrut +\mathstrut 3912q^{23} \) \(\mathstrut +\mathstrut 3186q^{24} \) \(\mathstrut -\mathstrut 3227q^{25} \) \(\mathstrut +\mathstrut 3416q^{26} \) \(\mathstrut -\mathstrut 2312q^{27} \) \(\mathstrut -\mathstrut 3087q^{28} \) \(\mathstrut +\mathstrut 10114q^{29} \) \(\mathstrut -\mathstrut 14608q^{30} \) \(\mathstrut -\mathstrut 7664q^{31} \) \(\mathstrut -\mathstrut 8849q^{32} \) \(\mathstrut +\mathstrut 16768q^{33} \) \(\mathstrut +\mathstrut 23154q^{34} \) \(\mathstrut +\mathstrut 1862q^{35} \) \(\mathstrut +\mathstrut 7433q^{36} \) \(\mathstrut -\mathstrut 4166q^{37} \) \(\mathstrut -\mathstrut 14230q^{38} \) \(\mathstrut -\mathstrut 18536q^{39} \) \(\mathstrut +\mathstrut 23376q^{40} \) \(\mathstrut -\mathstrut 24010q^{41} \) \(\mathstrut -\mathstrut 16562q^{42} \) \(\mathstrut +\mathstrut 7860q^{43} \) \(\mathstrut -\mathstrut 15040q^{44} \) \(\mathstrut +\mathstrut 7870q^{45} \) \(\mathstrut +\mathstrut 7344q^{46} \) \(\mathstrut +\mathstrut 21024q^{47} \) \(\mathstrut +\mathstrut 21278q^{48} \) \(\mathstrut +\mathstrut 7203q^{49} \) \(\mathstrut -\mathstrut 19811q^{50} \) \(\mathstrut +\mathstrut 31704q^{51} \) \(\mathstrut +\mathstrut 21924q^{52} \) \(\mathstrut +\mathstrut 11730q^{53} \) \(\mathstrut -\mathstrut 78508q^{54} \) \(\mathstrut -\mathstrut 51896q^{55} \) \(\mathstrut +\mathstrut 17199q^{56} \) \(\mathstrut +\mathstrut 14248q^{57} \) \(\mathstrut +\mathstrut 3134q^{58} \) \(\mathstrut -\mathstrut 46668q^{59} \) \(\mathstrut +\mathstrut 55328q^{60} \) \(\mathstrut -\mathstrut 39106q^{61} \) \(\mathstrut +\mathstrut 91740q^{62} \) \(\mathstrut +\mathstrut 29645q^{63} \) \(\mathstrut -\mathstrut 89151q^{64} \) \(\mathstrut +\mathstrut 46900q^{65} \) \(\mathstrut +\mathstrut 99296q^{66} \) \(\mathstrut -\mathstrut 23620q^{67} \) \(\mathstrut -\mathstrut 132090q^{68} \) \(\mathstrut -\mathstrut 128928q^{69} \) \(\mathstrut -\mathstrut 17444q^{70} \) \(\mathstrut +\mathstrut 38856q^{71} \) \(\mathstrut +\mathstrut 25695q^{72} \) \(\mathstrut +\mathstrut 85534q^{73} \) \(\mathstrut +\mathstrut 147414q^{74} \) \(\mathstrut +\mathstrut 40340q^{75} \) \(\mathstrut -\mathstrut 19446q^{76} \) \(\mathstrut +\mathstrut 8036q^{77} \) \(\mathstrut -\mathstrut 92680q^{78} \) \(\mathstrut +\mathstrut 83040q^{79} \) \(\mathstrut -\mathstrut 150016q^{80} \) \(\mathstrut -\mathstrut 106493q^{81} \) \(\mathstrut +\mathstrut 121282q^{82} \) \(\mathstrut +\mathstrut 97020q^{83} \) \(\mathstrut -\mathstrut 29498q^{84} \) \(\mathstrut +\mathstrut 58572q^{85} \) \(\mathstrut -\mathstrut 258848q^{86} \) \(\mathstrut -\mathstrut 111032q^{87} \) \(\mathstrut -\mathstrut 124176q^{88} \) \(\mathstrut +\mathstrut 33694q^{89} \) \(\mathstrut +\mathstrut 67532q^{90} \) \(\mathstrut -\mathstrut 10290q^{91} \) \(\mathstrut +\mathstrut 274944q^{92} \) \(\mathstrut +\mathstrut 14736q^{93} \) \(\mathstrut +\mathstrut 66228q^{94} \) \(\mathstrut +\mathstrut 29752q^{95} \) \(\mathstrut +\mathstrut 293986q^{96} \) \(\mathstrut -\mathstrut 37730q^{97} \) \(\mathstrut -\mathstrut 2401q^{98} \) \(\mathstrut -\mathstrut 27644q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(7))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 7
7.6.a.a \(1\) \(1.123\) \(\Q\) None \(-10\) \(-14\) \(-56\) \(-49\) \(+\) \(q-10q^{2}-14q^{3}+68q^{4}-56q^{5}+\cdots\)
7.6.a.b \(2\) \(1.123\) \(\Q(\sqrt{57}) \) None \(9\) \(-6\) \(-18\) \(98\) \(-\) \(q+(5-\beta )q^{2}+(-6+6\beta )q^{3}+(7-9\beta )q^{4}+\cdots\)