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Properties

Label 354.6.e
Level $354$
Weight $6$
Character orbit 354.e
Rep. character $\chi_{354}(7,\cdot)$
Character field $\Q(\zeta_{29})$
Dimension $1400$
Sturm bound $360$

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Defining parameters

Level: \( N \) \(=\) \( 354 = 2 \cdot 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 354.e (of order \(29\) and degree \(28\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 59 \)
Character field: \(\Q(\zeta_{29})\)
Sturm bound: \(360\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(354, [\chi])\).

Total New Old
Modular forms 8512 1400 7112
Cusp forms 8288 1400 6888
Eisenstein series 224 0 224

Trace form

\( 1400 q - 800 q^{4} + 72 q^{6} - 76 q^{7} - 4050 q^{9} + O(q^{10}) \) \( 1400 q - 800 q^{4} + 72 q^{6} - 76 q^{7} - 4050 q^{9} - 96 q^{10} + 752 q^{11} - 132 q^{13} - 1408 q^{14} - 396 q^{15} - 12800 q^{16} - 3144 q^{17} - 3728 q^{19} - 3344 q^{22} - 800 q^{23} + 1152 q^{24} - 29390 q^{25} - 1760 q^{26} - 1216 q^{28} - 12480 q^{29} + 3600 q^{30} + 14676 q^{31} - 360 q^{33} + 13600 q^{34} - 17768 q^{35} - 64800 q^{36} - 4220 q^{37} + 6400 q^{38} - 11160 q^{39} - 1536 q^{40} - 10216 q^{41} + 12672 q^{42} - 38420 q^{43} + 12032 q^{44} - 353936 q^{46} + 57564 q^{47} + 541202 q^{49} + 648864 q^{50} + 7992 q^{51} + 185344 q^{52} + 179192 q^{53} + 5832 q^{54} - 468900 q^{55} - 22528 q^{56} + 28656 q^{57} - 435120 q^{58} - 793100 q^{59} - 6336 q^{60} - 482580 q^{61} - 38224 q^{62} - 6156 q^{63} - 204800 q^{64} + 1065348 q^{65} - 27360 q^{66} + 1245788 q^{67} + 619712 q^{68} - 59688 q^{69} + 1115072 q^{70} + 678600 q^{71} - 658120 q^{73} - 1459984 q^{74} - 37728 q^{75} - 59648 q^{76} - 228176 q^{77} - 71712 q^{78} - 296420 q^{79} - 328050 q^{81} + 15808 q^{82} - 193784 q^{83} - 314616 q^{85} - 263680 q^{86} + 183060 q^{87} - 53504 q^{88} - 309040 q^{89} - 7776 q^{90} - 9456 q^{91} - 12800 q^{92} - 83628 q^{93} + 57312 q^{94} - 513272 q^{95} + 18432 q^{96} - 384692 q^{97} - 105472 q^{98} + 60912 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(354, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(354, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(354, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(59, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(118, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(177, [\chi])\)\(^{\oplus 2}\)