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Properties

Label 3549.2.co
Level $3549$
Weight $2$
Character orbit 3549.co
Rep. character $\chi_{3549}(64,\cdot)$
Character field $\Q(\zeta_{26})$
Dimension $2208$
Sturm bound $970$

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Defining parameters

Level: \( N \) \(=\) \( 3549 = 3 \cdot 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3549.co (of order \(26\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 169 \)
Character field: \(\Q(\zeta_{26})\)
Sturm bound: \(970\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3549, [\chi])\).

Total New Old
Modular forms 5856 2208 3648
Cusp forms 5760 2208 3552
Eisenstein series 96 0 96

Trace form

\( 2208 q + 188 q^{4} - 184 q^{9} + O(q^{10}) \) \( 2208 q + 188 q^{4} - 184 q^{9} + 4 q^{13} - 196 q^{16} - 16 q^{17} + 136 q^{22} + 8 q^{23} + 224 q^{25} - 20 q^{26} + 8 q^{29} + 8 q^{30} + 104 q^{31} + 260 q^{34} + 188 q^{36} - 56 q^{38} - 8 q^{39} - 40 q^{40} - 4 q^{42} + 32 q^{48} + 184 q^{49} + 24 q^{51} - 280 q^{52} - 28 q^{53} - 172 q^{55} + 52 q^{58} - 208 q^{60} + 8 q^{61} - 180 q^{62} + 188 q^{64} - 28 q^{65} + 192 q^{66} + 52 q^{67} + 16 q^{68} - 8 q^{69} - 16 q^{74} + 208 q^{76} + 16 q^{77} - 224 q^{78} - 8 q^{79} - 184 q^{81} - 220 q^{82} + 52 q^{85} + 176 q^{87} + 520 q^{88} + 4 q^{91} - 56 q^{92} + 152 q^{94} + 192 q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3549, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3549, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3549, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(507, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1183, [\chi])\)\(^{\oplus 2}\)