Properties

Label 294.6.p
Level $294$
Weight $6$
Character orbit 294.p
Rep. character $\chi_{294}(5,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $1128$
Sturm bound $336$

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Defining parameters

Level: \( N \) \(=\) \( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 294.p (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 147 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(336\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(294, [\chi])\).

Total New Old
Modular forms 3408 1128 2280
Cusp forms 3312 1128 2184
Eisenstein series 96 0 96

Trace form

\( 1128 q - 1504 q^{4} - 280 q^{6} + 154 q^{7} - 1520 q^{9} + O(q^{10}) \) \( 1128 q - 1504 q^{4} - 280 q^{6} + 154 q^{7} - 1520 q^{9} - 744 q^{10} - 2172 q^{15} + 24064 q^{16} - 496 q^{18} - 2652 q^{19} - 7236 q^{21} + 3560 q^{22} + 1920 q^{24} + 61932 q^{25} + 28182 q^{27} + 5024 q^{28} - 5504 q^{30} - 22458 q^{31} + 43542 q^{33} + 15200 q^{36} - 125044 q^{37} - 14204 q^{39} + 43648 q^{40} + 38000 q^{42} + 51144 q^{43} + 154210 q^{45} - 246480 q^{46} - 250434 q^{49} + 23820 q^{51} - 8256 q^{52} + 60408 q^{54} + 362278 q^{55} - 206494 q^{57} + 116240 q^{58} - 17376 q^{60} + 55412 q^{61} - 46560 q^{63} + 770048 q^{64} - 165312 q^{66} - 32704 q^{67} - 110572 q^{69} + 269584 q^{70} + 7936 q^{72} + 427596 q^{73} + 259644 q^{75} - 76736 q^{78} - 327674 q^{79} - 586132 q^{81} - 118176 q^{82} - 346656 q^{84} + 201232 q^{85} + 122018 q^{87} - 11392 q^{88} + 189672 q^{90} - 674084 q^{91} + 585970 q^{93} - 68384 q^{94} + 30720 q^{96} + 1527008 q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(294, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(294, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(294, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 2}\)