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Properties

Label 3483.2.co
Level $3483$
Weight $2$
Character orbit 3483.co
Rep. character $\chi_{3483}(64,\cdot)$
Character field $\Q(\zeta_{63})$
Dimension $4680$
Sturm bound $792$

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Defining parameters

Level: \( N \) \(=\) \( 3483 = 3^{4} \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3483.co (of order \(63\) and degree \(36\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1161 \)
Character field: \(\Q(\zeta_{63})\)
Sturm bound: \(792\)

Dimensions

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

Total New Old
Modular forms 14472 4824 9648
Cusp forms 14040 4680 9360
Eisenstein series 432 144 288

Trace form

\( 4680 q + 30 q^{2} - 30 q^{4} + 30 q^{5} - 72 q^{7} + 33 q^{8} + O(q^{10}) \) \( 4680 q + 30 q^{2} - 30 q^{4} + 30 q^{5} - 72 q^{7} + 33 q^{8} - 15 q^{10} + 36 q^{11} - 30 q^{13} - 42 q^{16} + 15 q^{17} - 15 q^{19} + 84 q^{20} + 15 q^{22} + 30 q^{23} - 30 q^{25} - 12 q^{26} - 60 q^{28} + 66 q^{29} - 30 q^{31} - 96 q^{32} + 3 q^{34} + 15 q^{35} - 36 q^{37} - 60 q^{38} - 84 q^{40} + 72 q^{41} - 45 q^{43} + 36 q^{44} - 15 q^{46} + 60 q^{47} - 108 q^{49} - 54 q^{50} - 6 q^{52} + 120 q^{53} - 60 q^{55} - 147 q^{56} - 30 q^{58} - 129 q^{59} - 66 q^{61} + 63 q^{62} + 333 q^{64} - 42 q^{65} - 48 q^{67} - 225 q^{68} + 135 q^{70} + 99 q^{71} - 33 q^{73} + 30 q^{74} + 54 q^{76} + 30 q^{77} - 72 q^{79} + 1248 q^{80} - 60 q^{82} - 18 q^{83} - 102 q^{85} + 429 q^{86} - 318 q^{88} + 69 q^{89} - 33 q^{91} + 84 q^{92} + 42 q^{94} + 90 q^{95} - 84 q^{97} + 69 q^{98} + O(q^{100}) \)

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

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