Properties

Label 91.10.r
Level $91$
Weight $10$
Character orbit 91.r
Rep. character $\chi_{91}(25,\cdot)$
Character field $\Q(\zeta_{6})$
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.r (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{6})\)
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

\( 164 q - 326 q^{3} + 20478 q^{4} - 513456 q^{9} + O(q^{10}) \) \( 164 q - 326 q^{3} + 20478 q^{4} - 513456 q^{9} + 37950 q^{10} + 328586 q^{12} + 205424 q^{13} - 347348 q^{14} - 5516922 q^{16} + 638792 q^{17} - 2021136 q^{22} - 3143742 q^{23} + 29660776 q^{25} - 4349148 q^{26} + 15971728 q^{27} + 11405516 q^{29} + 3318068 q^{30} - 13283874 q^{35} - 268857760 q^{36} + 41257144 q^{38} - 43335142 q^{39} - 64638572 q^{40} + 4428624 q^{42} + 208624280 q^{43} + 365752796 q^{48} - 8021754 q^{49} - 128665496 q^{51} + 116775564 q^{52} + 274651312 q^{53} + 333747724 q^{55} + 13700502 q^{56} + 205860820 q^{61} - 1213186480 q^{62} - 4080539840 q^{64} + 331150788 q^{65} - 1310285310 q^{66} - 598025264 q^{68} - 1943339932 q^{69} + 920056770 q^{74} + 1640230784 q^{75} + 1201037654 q^{77} + 2439213164 q^{78} - 335791710 q^{79} - 4192022058 q^{81} - 617219896 q^{82} - 3240850496 q^{87} + 1326885718 q^{88} + 14332940596 q^{90} - 3162562236 q^{91} - 7831634604 q^{92} + 1733533760 q^{94} + 319654502 q^{95} + O(q^{100}) \)

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.r.a $164$ $46.868$ None \(0\) \(-326\) \(0\) \(0\)