Properties

Label 7.9.b
Level 7
Weight 9
Character orbit b
Rep. character \(\chi_{7}(6,\cdot)\)
Character field \(\Q\)
Dimension 5
Newforms 2
Sturm bound 6
Trace bound 1

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Defining parameters

Level: \( N \) = \( 7 \)
Weight: \( k \) = \( 9 \)
Character orbit: \([\chi]\) = 7.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 7 \)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(6\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(7, [\chi])\).

Total New Old
Modular forms 7 7 0
Cusp forms 5 5 0
Eisenstein series 2 2 0

Trace form

\(5q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 673q^{4} \) \(\mathstrut +\mathstrut 3829q^{7} \) \(\mathstrut -\mathstrut 10591q^{8} \) \(\mathstrut -\mathstrut 1563q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(5q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 673q^{4} \) \(\mathstrut +\mathstrut 3829q^{7} \) \(\mathstrut -\mathstrut 10591q^{8} \) \(\mathstrut -\mathstrut 1563q^{9} \) \(\mathstrut -\mathstrut 9014q^{11} \) \(\mathstrut +\mathstrut 24577q^{14} \) \(\mathstrut +\mathstrut 72960q^{15} \) \(\mathstrut +\mathstrut 185729q^{16} \) \(\mathstrut -\mathstrut 581919q^{18} \) \(\mathstrut +\mathstrut 545664q^{21} \) \(\mathstrut -\mathstrut 635166q^{22} \) \(\mathstrut +\mathstrut 887146q^{23} \) \(\mathstrut -\mathstrut 1665115q^{25} \) \(\mathstrut +\mathstrut 3082625q^{28} \) \(\mathstrut -\mathstrut 1364822q^{29} \) \(\mathstrut +\mathstrut 4712640q^{30} \) \(\mathstrut -\mathstrut 8795295q^{32} \) \(\mathstrut +\mathstrut 2304960q^{35} \) \(\mathstrut -\mathstrut 326079q^{36} \) \(\mathstrut +\mathstrut 4641386q^{37} \) \(\mathstrut -\mathstrut 9276288q^{39} \) \(\mathstrut +\mathstrut 5880000q^{42} \) \(\mathstrut -\mathstrut 977974q^{43} \) \(\mathstrut +\mathstrut 8650146q^{44} \) \(\mathstrut +\mathstrut 3509058q^{46} \) \(\mathstrut +\mathstrut 4570181q^{49} \) \(\mathstrut -\mathstrut 13077215q^{50} \) \(\mathstrut -\mathstrut 21727872q^{51} \) \(\mathstrut +\mathstrut 22127338q^{53} \) \(\mathstrut -\mathstrut 44142847q^{56} \) \(\mathstrut +\mathstrut 33733440q^{57} \) \(\mathstrut -\mathstrut 32304606q^{58} \) \(\mathstrut +\mathstrut 65479680q^{60} \) \(\mathstrut -\mathstrut 24458091q^{63} \) \(\mathstrut +\mathstrut 34582081q^{64} \) \(\mathstrut -\mathstrut 39184320q^{65} \) \(\mathstrut +\mathstrut 54187786q^{67} \) \(\mathstrut -\mathstrut 71359680q^{70} \) \(\mathstrut +\mathstrut 7568746q^{71} \) \(\mathstrut -\mathstrut 55440831q^{72} \) \(\mathstrut +\mathstrut 139883618q^{74} \) \(\mathstrut +\mathstrut 17713066q^{77} \) \(\mathstrut -\mathstrut 99960000q^{78} \) \(\mathstrut -\mathstrut 146774102q^{79} \) \(\mathstrut -\mathstrut 32375547q^{81} \) \(\mathstrut +\mathstrut 19869696q^{84} \) \(\mathstrut +\mathstrut 108466560q^{85} \) \(\mathstrut +\mathstrut 382302818q^{86} \) \(\mathstrut -\mathstrut 194727774q^{88} \) \(\mathstrut +\mathstrut 206157504q^{91} \) \(\mathstrut -\mathstrut 92484990q^{92} \) \(\mathstrut -\mathstrut 90960000q^{93} \) \(\mathstrut -\mathstrut 424874880q^{95} \) \(\mathstrut -\mathstrut 63195839q^{98} \) \(\mathstrut +\mathstrut 152647050q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(7, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
7.9.b.a \(1\) \(2.852\) \(\Q\) \(\Q(\sqrt{-7}) \) \(-31\) \(0\) \(0\) \(2401\) \(q-31q^{2}+705q^{4}+7^{4}q^{7}-13919q^{8}+\cdots\)
7.9.b.b \(4\) \(2.852\) \(\mathbb{Q}[x]/(x^{4} + \cdots)\) None \(32\) \(0\) \(0\) \(1428\) \(q+(8+\beta _{3})q^{2}-\beta _{1}q^{3}+(-8+2^{4}\beta _{3})q^{4}+\cdots\)