Properties

Label 91.10.i
Level $91$
Weight $10$
Character orbit 91.i
Rep. character $\chi_{91}(34,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $164$
Newform subspaces $1$
Sturm bound $93$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 91 = 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 91.i (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(93\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(91, [\chi])\).

Total New Old
Modular forms 172 172 0
Cusp forms 164 164 0
Eisenstein series 8 8 0

Trace form

\( 164 q - 4 q^{2} - 1142 q^{7} + 2044 q^{8} - 1023524 q^{9} + O(q^{10}) \) \( 164 q - 4 q^{2} - 1142 q^{7} + 2044 q^{8} - 1023524 q^{9} + 83020 q^{11} + 342380 q^{14} + 108440 q^{15} - 9961480 q^{16} + 733960 q^{18} - 2430528 q^{21} - 2436232 q^{22} - 3224028 q^{28} - 12730912 q^{29} + 14102504 q^{32} + 1383128 q^{35} - 22260172 q^{37} + 7370608 q^{39} + 142705660 q^{42} - 29990964 q^{44} - 340921064 q^{46} - 250003828 q^{50} + 408277152 q^{53} + 172857368 q^{57} - 25520428 q^{58} + 541182148 q^{60} - 173245586 q^{63} + 743607836 q^{65} + 460418836 q^{67} - 1611790784 q^{70} - 937506828 q^{71} - 1730965108 q^{72} + 1230722160 q^{74} + 2491131268 q^{78} + 324907200 q^{79} + 7601803508 q^{81} - 4681602688 q^{84} - 700010456 q^{85} - 108608508 q^{86} - 750548542 q^{91} - 1994311080 q^{92} + 491721312 q^{93} - 6546627460 q^{98} - 6566823268 q^{99} + O(q^{100}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(91, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
91.10.i.a $164$ $46.868$ None \(-4\) \(0\) \(0\) \(-1142\)