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Properties

Label 7.15.b
Level $7$
Weight $15$
Character orbit 7.b
Rep. character $\chi_{7}(6,\cdot)$
Character field $\Q$
Dimension $9$
Newform subspaces $2$
Sturm bound $10$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 7 \)
Weight: \( k \) \(=\) \( 15 \)
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: \(10\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{15}(7, [\chi])\).

Total New Old
Modular forms 11 11 0
Cusp forms 9 9 0
Eisenstein series 2 2 0

Trace form

\( 9 q + 89 q^{2} + 74001 q^{4} + 652113 q^{7} + 5008825 q^{8} - 22748991 q^{9} + O(q^{10}) \) \( 9 q + 89 q^{2} + 74001 q^{4} + 652113 q^{7} + 5008825 q^{8} - 22748991 q^{9} - 13666342 q^{11} - 256065439 q^{14} + 358604160 q^{15} + 797297697 q^{16} - 2316096879 q^{18} - 3461974656 q^{21} + 15496407930 q^{22} - 1266151294 q^{23} - 5724106575 q^{25} - 21975091047 q^{28} - 58637148790 q^{29} + 28450320000 q^{30} + 72114536649 q^{32} + 191911251840 q^{35} - 142324780023 q^{36} - 217964795526 q^{37} + 498015493248 q^{39} - 800893726080 q^{42} - 118813043814 q^{43} + 281922752682 q^{44} + 591477340578 q^{46} - 2067596107815 q^{49} + 3421642555265 q^{50} - 2130176489472 q^{51} + 1312114360154 q^{53} - 5391834400127 q^{56} + 3524551966080 q^{57} - 12690176810070 q^{58} + 34054684231680 q^{60} - 12503128840503 q^{63} - 8494633223247 q^{64} - 20955121299840 q^{65} + 42693010493514 q^{67} - 34600029179520 q^{70} + 21030931108898 q^{71} - 113128972275855 q^{72} + 128769670714522 q^{74} - 77460334258006 q^{77} + 121635975377280 q^{78} - 74008008249870 q^{79} + 196974865248057 q^{81} - 315335206803456 q^{84} + 58215702758400 q^{85} - 243211564558022 q^{86} + 422359745894202 q^{88} - 98358431773056 q^{91} + 153085992329874 q^{92} - 363290481600000 q^{93} + 396115416984960 q^{95} - 201327798086359 q^{98} - 176904458351862 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{15}^{\mathrm{new}}(7, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
7.15.b.a 7.b 7.b $1$ $8.703$ \(\Q\) \(\Q(\sqrt{-7}) \) \(-87\) \(0\) \(0\) \(-823543\) $\mathrm{U}(1)[D_{2}]$ \(q-87q^{2}-8815q^{4}-7^{7}q^{7}+2192313q^{8}+\cdots\)
7.15.b.b 7.b 7.b $8$ $8.703$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(176\) \(0\) \(0\) \(1475656\) $\mathrm{SU}(2)[C_{2}]$ \(q+(22+\beta _{2})q^{2}-\beta _{3}q^{3}+(10352+\beta _{1}+\cdots)q^{4}+\cdots\)