Properties

Label 96.10.c
Level $96$
Weight $10$
Character orbit 96.c
Rep. character $\chi_{96}(95,\cdot)$
Character field $\Q$
Dimension $36$
Newform subspaces $1$
Sturm bound $160$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 96 = 2^{5} \cdot 3 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 96.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 12 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(160\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(96, [\chi])\).

Total New Old
Modular forms 152 36 116
Cusp forms 136 36 100
Eisenstein series 16 0 16

Trace form

\( 36 q - 27740 q^{9} + O(q^{10}) \) \( 36 q - 27740 q^{9} + 194616 q^{13} + 634168 q^{21} - 13299948 q^{25} + 9661040 q^{33} - 16866216 q^{37} + 35926304 q^{45} - 152499348 q^{49} + 261857496 q^{57} - 497603016 q^{61} - 1087284512 q^{69} - 840635352 q^{73} - 1155854332 q^{81} + 348272640 q^{85} - 1080661448 q^{93} + 820514664 q^{97} + O(q^{100}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(96, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
96.10.c.a 96.c 12.b $36$ $49.443$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{10}^{\mathrm{old}}(96, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(96, [\chi]) \cong \) \(S_{10}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)