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Properties

Label 1911.2.r
Level $1911$
Weight $2$
Character orbit 1911.r
Rep. character $\chi_{1911}(68,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $358$
Sturm bound $522$

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Defining parameters

Level: \( N \) \(=\) \( 1911 = 3 \cdot 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1911.r (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 273 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(522\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1911, [\chi])\).

Total New Old
Modular forms 554 390 164
Cusp forms 490 358 132
Eisenstein series 64 32 32

Trace form

\( 358 q + 3 q^{3} - 340 q^{4} - 12 q^{6} + 3 q^{9} + O(q^{10}) \) \( 358 q + 3 q^{3} - 340 q^{4} - 12 q^{6} + 3 q^{9} + 6 q^{10} - 10 q^{13} + 13 q^{15} + 312 q^{16} + 14 q^{18} + 21 q^{19} - 22 q^{22} + 18 q^{24} - 145 q^{25} - 48 q^{30} + 39 q^{31} + 45 q^{33} - 20 q^{36} - 6 q^{37} - 50 q^{39} - 90 q^{40} + 18 q^{43} + 104 q^{46} + 18 q^{48} - 12 q^{51} + 52 q^{52} + 18 q^{55} + 26 q^{57} - 50 q^{58} - 15 q^{60} + 45 q^{61} - 212 q^{64} - 75 q^{66} - q^{67} - 33 q^{69} - 81 q^{72} - 60 q^{73} - 12 q^{76} + 55 q^{78} - 17 q^{79} - 9 q^{81} + 18 q^{82} - 22 q^{85} + 82 q^{88} + 6 q^{93} - 36 q^{94} - 30 q^{96} + 33 q^{97} - 58 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1911, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1911, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1911, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)