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Properties

Label 3450.2.bk
Level $3450$
Weight $2$
Character orbit 3450.bk
Rep. character $\chi_{3450}(31,\cdot)$
Character field $\Q(\zeta_{55})$
Dimension $4800$
Sturm bound $1440$

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Defining parameters

Level: \( N \) \(=\) \( 3450 = 2 \cdot 3 \cdot 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3450.bk (of order \(55\) and degree \(40\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 575 \)
Character field: \(\Q(\zeta_{55})\)
Sturm bound: \(1440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3450, [\chi])\).

Total New Old
Modular forms 29120 4800 24320
Cusp forms 28480 4800 23680
Eisenstein series 640 0 640

Trace form

\( 4800 q + 120 q^{4} - 8 q^{5} - 16 q^{7} + 120 q^{9} + O(q^{10}) \) \( 4800 q + 120 q^{4} - 8 q^{5} - 16 q^{7} + 120 q^{9} + 24 q^{11} - 16 q^{13} - 8 q^{15} + 120 q^{16} + 24 q^{17} + 16 q^{19} + 36 q^{20} - 8 q^{21} + 24 q^{22} - 228 q^{23} + 88 q^{25} + 72 q^{28} + 48 q^{29} + 32 q^{30} + 24 q^{33} - 16 q^{34} - 8 q^{35} + 120 q^{36} + 72 q^{37} - 32 q^{38} + 64 q^{43} - 16 q^{44} - 8 q^{45} + 12 q^{46} - 256 q^{47} - 496 q^{49} - 24 q^{50} + 32 q^{51} - 16 q^{52} + 48 q^{53} + 44 q^{55} + 72 q^{57} + 48 q^{59} - 8 q^{60} - 40 q^{61} + 56 q^{62} + 24 q^{63} + 120 q^{64} - 40 q^{65} - 16 q^{66} - 48 q^{67} - 16 q^{68} - 8 q^{69} + 96 q^{70} + 24 q^{71} + 56 q^{73} - 32 q^{75} + 16 q^{76} - 80 q^{77} - 16 q^{78} + 16 q^{79} - 8 q^{80} + 120 q^{81} + 112 q^{82} - 8 q^{83} - 8 q^{84} + 40 q^{85} - 48 q^{86} - 24 q^{87} - 16 q^{88} + 200 q^{91} - 24 q^{92} + 32 q^{93} - 16 q^{94} - 220 q^{95} - 24 q^{97} + 144 q^{98} + 72 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3450, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3450, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3450, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(575, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1150, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1725, [\chi])\)\(^{\oplus 2}\)