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Properties

Label 3381.2.z
Level $3381$
Weight $2$
Character orbit 3381.z
Rep. character $\chi_{3381}(277,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $2472$
Sturm bound $896$

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Defining parameters

Level: \( N \) \(=\) \( 3381 = 3 \cdot 7^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3381.z (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{21})\)
Sturm bound: \(896\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3381, [\chi])\).

Total New Old
Modular forms 5424 2472 2952
Cusp forms 5328 2472 2856
Eisenstein series 96 0 96

Trace form

\( 2472 q - 2 q^{3} + 208 q^{4} + 8 q^{6} - 6 q^{7} - 24 q^{8} + 206 q^{9} + O(q^{10}) \) \( 2472 q - 2 q^{3} + 208 q^{4} + 8 q^{6} - 6 q^{7} - 24 q^{8} + 206 q^{9} + 16 q^{10} - 4 q^{12} + 4 q^{13} + 12 q^{14} + 20 q^{15} + 228 q^{16} + 8 q^{17} + 6 q^{19} + 16 q^{20} + 8 q^{21} - 20 q^{22} + 84 q^{24} + 222 q^{25} - 32 q^{26} + 4 q^{27} + 56 q^{28} - 24 q^{29} + 146 q^{31} + 192 q^{32} + 12 q^{33} + 128 q^{34} - 4 q^{35} - 416 q^{36} + 80 q^{37} - 92 q^{38} - 16 q^{39} - 132 q^{40} - 64 q^{41} - 16 q^{42} + 12 q^{43} + 128 q^{44} - 20 q^{47} - 96 q^{48} - 50 q^{49} - 24 q^{50} - 168 q^{52} - 80 q^{53} - 4 q^{54} + 160 q^{55} + 8 q^{56} - 12 q^{57} + 60 q^{58} - 36 q^{59} - 156 q^{60} + 2 q^{61} - 136 q^{62} + 20 q^{63} - 376 q^{64} + 12 q^{65} + 24 q^{66} + 26 q^{67} + 12 q^{68} + 16 q^{69} + 12 q^{70} + 152 q^{71} + 96 q^{72} - 18 q^{73} + 60 q^{74} - 14 q^{75} + 60 q^{76} - 8 q^{77} + 16 q^{78} + 26 q^{79} - 176 q^{80} + 206 q^{81} - 24 q^{82} + 28 q^{83} - 4 q^{84} + 32 q^{85} - 332 q^{86} + 8 q^{87} - 344 q^{88} - 140 q^{89} - 32 q^{90} - 10 q^{91} + 6 q^{93} + 20 q^{94} - 392 q^{95} + 164 q^{96} - 40 q^{97} - 268 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3381, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3381, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3381, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1127, [\chi])\)\(^{\oplus 2}\)