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Properties

Label 3483.2.bm
Level $3483$
Weight $2$
Character orbit 3483.bm
Rep. character $\chi_{3483}(379,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $2088$
Sturm bound $792$

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Defining parameters

Level: \( N \) \(=\) \( 3483 = 3^{4} \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3483.bm (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 387 \)
Character field: \(\Q(\zeta_{21})\)
Sturm bound: \(792\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3483, [\chi])\).

Total New Old
Modular forms 4896 2136 2760
Cusp forms 4608 2088 2520
Eisenstein series 288 48 240

Trace form

\( 2088 q + 182 q^{4} + 34 q^{7} + O(q^{10}) \) \( 2088 q + 182 q^{4} + 34 q^{7} - 4 q^{10} + 20 q^{13} + 170 q^{16} - 100 q^{19} + 32 q^{22} + 176 q^{25} - 164 q^{28} - 90 q^{31} + 32 q^{34} - 68 q^{37} - 34 q^{40} + 26 q^{43} + 44 q^{46} - 962 q^{49} - 114 q^{52} + 20 q^{55} + 2 q^{58} - 16 q^{61} - 292 q^{64} - 4 q^{67} + 28 q^{70} + 56 q^{73} - 10 q^{76} + 34 q^{79} + 20 q^{82} + 4 q^{85} + 192 q^{88} - 236 q^{91} + 98 q^{94} - 16 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3483, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3483, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3483, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(387, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1161, [\chi])\)\(^{\oplus 2}\)