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Properties

Label 1550.3.n
Level $1550$
Weight $3$
Character orbit 1550.n
Rep. character $\chi_{1550}(99,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $192$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 1550 = 2 \cdot 5^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1550.n (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 155 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1550, [\chi])\).

Total New Old
Modular forms 984 192 792
Cusp forms 936 192 744
Eisenstein series 48 0 48

Trace form

\( 192 q - 384 q^{4} - 328 q^{9} + O(q^{10}) \) \( 192 q - 384 q^{4} - 328 q^{9} + 768 q^{16} - 4 q^{19} - 36 q^{21} - 184 q^{31} + 96 q^{34} + 656 q^{36} + 80 q^{39} - 44 q^{41} + 812 q^{49} - 108 q^{51} - 76 q^{59} - 1536 q^{64} + 128 q^{66} + 224 q^{69} + 196 q^{71} - 288 q^{74} + 8 q^{76} + 936 q^{79} - 1584 q^{81} + 72 q^{84} + 312 q^{86} - 352 q^{94} + 216 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(1550, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(1550, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1550, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(155, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(310, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(775, [\chi])\)\(^{\oplus 2}\)