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Properties

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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
7.9.b.a 7.b 7.b $1$ $2.852$ \(\Q\) \(\Q(\sqrt{-7}) \) \(-31\) \(0\) \(0\) \(2401\) $\mathrm{U}(1)[D_{2}]$ \(q-31q^{2}+705q^{4}+7^{4}q^{7}-13919q^{8}+\cdots\)
7.9.b.b 7.b 7.b $4$ $2.852$ \(\mathbb{Q}[x]/(x^{4} + \cdots)\) None \(32\) \(0\) \(0\) \(1428\) $\mathrm{SU}(2)[C_{2}]$ \(q+(8+\beta _{3})q^{2}-\beta _{1}q^{3}+(-8+2^{4}\beta _{3})q^{4}+\cdots\)