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Properties

Label 3549.2.cu
Level $3549$
Weight $2$
Character orbit 3549.cu
Rep. character $\chi_{3549}(34,\cdot)$
Character field $\Q(\zeta_{52})$
Dimension $5856$
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.cu (of order \(52\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1183 \)
Character field: \(\Q(\zeta_{52})\)
Sturm bound: \(970\)

Dimensions

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

Total New Old
Modular forms 11712 5856 5856
Cusp forms 11520 5856 5664
Eisenstein series 192 0 192

Trace form

\( 5856 q - 4 q^{7} + 488 q^{9} + O(q^{10}) \) \( 5856 q - 4 q^{7} + 488 q^{9} - 16 q^{11} + 32 q^{14} + 512 q^{16} - 12 q^{21} - 4 q^{28} + 480 q^{32} + 16 q^{35} + 24 q^{39} + 24 q^{42} - 16 q^{44} + 8 q^{46} - 40 q^{50} - 40 q^{57} - 48 q^{58} + 16 q^{60} + 4 q^{63} - 16 q^{65} - 360 q^{67} - 192 q^{70} - 24 q^{71} - 384 q^{74} - 32 q^{78} - 488 q^{81} - 36 q^{84} + 456 q^{85} + 576 q^{86} - 36 q^{91} - 144 q^{92} - 40 q^{93} - 120 q^{98} + 16 q^{99} + O(q^{100}) \)

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

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