Properties

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

Related objects

Downloads

Learn more about

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: \(\Q\)
Newform subspaces: \( 2 \)
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

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

Decomposition of \(S_{9}^{\mathrm{new}}(7, [\chi])\) into newform subspaces

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 \(32\) \(0\) \(0\) \(1428\) \(q+(8+\beta _{3})q^{2}-\beta _{1}q^{3}+(-8+2^{4}\beta _{3})q^{4}+\cdots\)