Properties

Label 84.12.b
Level $84$
Weight $12$
Character orbit 84.b
Rep. character $\chi_{84}(55,\cdot)$
Character field $\Q$
Dimension $88$
Newform subspaces $2$
Sturm bound $192$
Trace bound $3$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 84.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(192\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(84, [\chi])\).

Total New Old
Modular forms 180 88 92
Cusp forms 172 88 84
Eisenstein series 8 0 8

Trace form

\( 88 q - 46 q^{2} + 3082 q^{4} - 37390 q^{8} + 5196312 q^{9} + O(q^{10}) \) \( 88 q - 46 q^{2} + 3082 q^{4} - 37390 q^{8} + 5196312 q^{9} + 1258394 q^{14} - 8825518 q^{16} - 2716254 q^{18} + 65124 q^{21} - 35982924 q^{22} - 907257392 q^{25} + 148166010 q^{28} - 155346416 q^{29} + 402614064 q^{30} - 386265726 q^{32} + 181989018 q^{36} + 682743768 q^{37} - 1734615648 q^{42} - 1760267332 q^{44} - 3550105956 q^{46} - 1639234000 q^{49} + 4316466298 q^{50} + 3829614304 q^{53} - 17151189734 q^{56} - 3393763272 q^{57} + 10169667500 q^{58} + 21586714488 q^{60} - 24134216798 q^{64} - 11249650000 q^{65} + 41702531240 q^{70} - 2207842110 q^{72} - 81845269556 q^{74} - 4186698224 q^{77} + 47746438200 q^{78} + 306837027288 q^{81} - 59751293328 q^{84} + 210304255256 q^{85} + 485929727196 q^{86} + 437789349676 q^{88} + 202679719060 q^{92} - 176616661248 q^{93} + 80110669938 q^{98} + O(q^{100}) \)

Decomposition of \(S_{12}^{\mathrm{new}}(84, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
84.12.b.a 84.b 28.d $44$ $64.541$ None \(-23\) \(-10692\) \(0\) \(-134\) $\mathrm{SU}(2)[C_{2}]$
84.12.b.b 84.b 28.d $44$ $64.541$ None \(-23\) \(10692\) \(0\) \(134\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{12}^{\mathrm{old}}(84, [\chi])\) into lower level spaces

\( S_{12}^{\mathrm{old}}(84, [\chi]) \cong \) \(S_{12}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 2}\)