Properties

Label 91.10.c
Level $91$
Weight $10$
Character orbit 91.c
Rep. character $\chi_{91}(64,\cdot)$
Character field $\Q$
Dimension $62$
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.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q\)
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 86 62 24
Cusp forms 82 62 20
Eisenstein series 4 0 4

Trace form

\( 62 q - 15360 q^{4} + 378842 q^{9} + O(q^{10}) \) \( 62 q - 15360 q^{4} + 378842 q^{9} - 129080 q^{10} - 86340 q^{12} + 212162 q^{13} - 153664 q^{14} + 4327304 q^{16} + 1652452 q^{17} - 5012396 q^{22} - 1278096 q^{23} - 9442150 q^{25} - 10907340 q^{26} + 16794384 q^{27} - 10363760 q^{29} + 8275336 q^{30} - 8902908 q^{35} - 157163812 q^{36} + 7473860 q^{38} - 45113592 q^{39} + 6264340 q^{40} - 12446784 q^{42} + 112595748 q^{43} - 235575712 q^{48} - 357417662 q^{49} + 76280072 q^{51} + 184926780 q^{52} + 163068704 q^{53} - 171698952 q^{55} + 118013952 q^{56} + 528120292 q^{61} + 327058744 q^{62} - 1108215168 q^{64} + 430577400 q^{65} + 1069507908 q^{66} - 760577284 q^{68} - 154846856 q^{69} - 2010119892 q^{74} + 881911824 q^{75} + 19918696 q^{77} + 251736268 q^{78} + 114047552 q^{79} + 50540630 q^{81} - 3357122608 q^{82} - 7796519536 q^{87} + 6249329764 q^{88} + 2721868364 q^{90} + 601248816 q^{91} + 6449180076 q^{92} - 5238038284 q^{94} + 504345292 q^{95} + O(q^{100}) \)

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.c.a $62$ $46.868$ None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{10}^{\mathrm{old}}(91, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(91, [\chi]) \cong \) \(S_{10}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 2}\)