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Properties

Label 84.12.i
Level $84$
Weight $12$
Character orbit 84.i
Rep. character $\chi_{84}(25,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $30$
Newform subspaces $2$
Sturm bound $192$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 84.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 2 \)
Sturm bound: \(192\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 364 30 334
Cusp forms 340 30 310
Eisenstein series 24 0 24

Trace form

\( 30 q - 243 q^{3} + 5062 q^{5} + 85513 q^{7} - 885735 q^{9} + O(q^{10}) \) \( 30 q - 243 q^{3} + 5062 q^{5} + 85513 q^{7} - 885735 q^{9} - 168346 q^{11} + 4238158 q^{13} + 4555764 q^{15} + 6593480 q^{17} - 15965379 q^{19} - 14946444 q^{21} + 11152856 q^{23} - 253592513 q^{25} + 28697814 q^{27} + 220952344 q^{29} + 353259565 q^{31} - 67370778 q^{33} - 198601390 q^{35} + 275343963 q^{37} - 141935571 q^{39} - 2509437324 q^{41} - 609947346 q^{43} + 298906038 q^{45} + 1737627882 q^{47} - 1085650227 q^{49} + 883479960 q^{51} + 5821874196 q^{53} + 8781694760 q^{55} - 14476234626 q^{57} - 7143324308 q^{59} - 10321651694 q^{61} + 232121619 q^{63} - 22458380106 q^{65} - 17540653753 q^{67} + 55369144080 q^{69} + 32665617452 q^{71} - 13975394635 q^{73} - 31424816133 q^{75} + 11855738104 q^{77} - 4627274045 q^{79} - 52301766015 q^{81} - 273360841036 q^{83} + 9336802592 q^{85} - 2035961892 q^{87} + 11090344608 q^{89} - 124798679231 q^{91} - 5817722535 q^{93} + 240298918862 q^{95} + 127867387388 q^{97} + 19881325908 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.i.a 84.i 7.c $14$ $64.541$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(1701\) \(7218\) \(35001\) $\mathrm{SU}(2)[C_{3}]$ \(q+(3^{5}+3^{5}\beta _{1})q^{3}+(-1031\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\)
84.12.i.b 84.i 7.c $16$ $64.541$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(-1944\) \(-2156\) \(50512\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-3^{5}+3^{5}\beta _{1})q^{3}+(-269\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots\)

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

\( S_{12}^{\mathrm{old}}(84, [\chi]) \cong \) \(S_{12}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)