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Properties

Label 178.6.c
Level $178$
Weight $6$
Character orbit 178.c
Rep. character $\chi_{178}(55,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $74$
Newform subspaces $2$
Sturm bound $135$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 178 = 2 \cdot 89 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 178.c (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 89 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(135\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(178, [\chi])\).

Total New Old
Modular forms 230 74 156
Cusp forms 222 74 148
Eisenstein series 8 0 8

Trace form

\( 74 q - 8 q^{2} - 26 q^{3} + 1184 q^{4} - 88 q^{6} - 128 q^{8} + O(q^{10}) \) \( 74 q - 8 q^{2} - 26 q^{3} + 1184 q^{4} - 88 q^{6} - 128 q^{8} + 444 q^{11} - 416 q^{12} - 1056 q^{13} - 800 q^{14} - 728 q^{15} + 18944 q^{16} - 402 q^{19} - 1840 q^{22} + 8484 q^{23} - 1408 q^{24} - 57742 q^{25} - 5328 q^{26} + 20800 q^{27} + 4340 q^{29} - 15952 q^{30} + 20184 q^{31} - 2048 q^{32} + 3468 q^{33} - 4852 q^{35} + 12916 q^{37} - 3512 q^{38} + 31160 q^{39} - 11726 q^{41} + 61970 q^{43} + 7104 q^{44} - 168236 q^{45} - 18720 q^{46} - 6656 q^{48} - 13064 q^{50} - 41676 q^{51} - 16896 q^{52} + 24176 q^{54} - 12800 q^{56} + 144268 q^{57} - 107520 q^{58} + 83510 q^{59} - 11648 q^{60} - 9200 q^{61} + 18672 q^{62} - 234684 q^{63} + 303104 q^{64} - 228176 q^{65} + 53968 q^{66} - 65916 q^{67} + 11600 q^{70} - 92288 q^{73} - 31136 q^{74} - 213286 q^{75} - 6432 q^{76} + 34024 q^{77} - 114240 q^{78} - 622326 q^{81} - 55496 q^{82} + 321510 q^{83} + 238496 q^{85} + 12344 q^{86} + 862032 q^{87} - 29440 q^{88} + 107526 q^{89} + 273840 q^{90} + 312064 q^{91} + 135744 q^{92} + 557584 q^{93} + 246892 q^{95} - 22528 q^{96} - 343892 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(178, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
178.6.c.a 178.c 89.c $36$ $28.548$ None 178.6.c.a \(144\) \(-24\) \(0\) \(-100\) $\mathrm{SU}(2)[C_{4}]$
178.6.c.b 178.c 89.c $38$ $28.548$ None 178.6.c.b \(-152\) \(-2\) \(0\) \(100\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{6}^{\mathrm{old}}(178, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(178, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(89, [\chi])\)\(^{\oplus 2}\)