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Properties

Label 546.8.i
Level $546$
Weight $8$
Character orbit 546.i
Rep. character $\chi_{546}(79,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $224$
Sturm bound $896$

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Defining parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 546.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(896\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(546, [\chi])\).

Total New Old
Modular forms 1584 224 1360
Cusp forms 1552 224 1328
Eisenstein series 32 0 32

Trace form

\( 224 q - 7168 q^{4} + 8 q^{5} - 1728 q^{6} - 2924 q^{7} - 81648 q^{9} + O(q^{10}) \) \( 224 q - 7168 q^{4} + 8 q^{5} - 1728 q^{6} - 2924 q^{7} - 81648 q^{9} - 416 q^{10} - 15448 q^{11} - 17576 q^{13} - 3616 q^{14} + 42552 q^{15} - 458752 q^{16} + 122796 q^{17} + 54872 q^{19} - 1024 q^{20} + 110080 q^{22} + 179040 q^{23} + 55296 q^{24} - 1966316 q^{25} + 115456 q^{28} + 1317528 q^{29} - 157248 q^{30} + 151668 q^{31} + 415908 q^{33} - 1030272 q^{34} - 1375608 q^{35} + 10450944 q^{36} + 464640 q^{37} + 273440 q^{38} - 26624 q^{40} + 3247168 q^{41} + 977184 q^{42} - 2675616 q^{43} - 988672 q^{44} + 5832 q^{45} + 1021888 q^{46} + 555768 q^{47} + 111872 q^{49} - 2340608 q^{50} - 96984 q^{51} + 562432 q^{52} + 3359796 q^{53} + 629856 q^{54} + 14463688 q^{55} - 231424 q^{56} - 4829328 q^{57} - 382944 q^{58} - 11956224 q^{59} - 1361664 q^{60} + 2846084 q^{61} - 1555328 q^{62} + 816480 q^{63} + 58720256 q^{64} + 3567928 q^{65} + 3430352 q^{67} + 7858944 q^{68} + 2075328 q^{69} + 4941344 q^{70} + 10116480 q^{71} + 10399072 q^{73} - 4952064 q^{74} - 7023616 q^{76} - 33915176 q^{77} - 3922932 q^{79} + 32768 q^{80} - 59521392 q^{81} + 20500480 q^{82} - 60426240 q^{83} + 17415040 q^{85} - 11277952 q^{86} + 9613188 q^{87} - 3522560 q^{88} - 28781104 q^{89} + 606528 q^{90} - 8401328 q^{91} - 22917120 q^{92} - 4062744 q^{93} + 4080416 q^{94} + 24562728 q^{95} + 3538944 q^{96} - 48611960 q^{97} + 21154176 q^{98} + 22523184 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(546, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{8}^{\mathrm{old}}(546, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(546, [\chi]) \cong \) \(S_{8}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)