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Properties

Label 1550.3.v
Level $1550$
Weight $3$
Character orbit 1550.v
Rep. character $\chi_{1550}(399,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $384$
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.v (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 155 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(720\)

Dimensions

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

Total New Old
Modular forms 1968 384 1584
Cusp forms 1872 384 1488
Eisenstein series 96 0 96

Trace form

\( 384 q + 192 q^{4} - 328 q^{9} + O(q^{10}) \) \( 384 q + 192 q^{4} - 328 q^{9} - 384 q^{16} + 8 q^{19} + 60 q^{21} - 40 q^{29} + 164 q^{31} + 160 q^{34} - 2224 q^{36} - 220 q^{39} - 336 q^{41} - 320 q^{46} + 664 q^{49} - 48 q^{51} - 680 q^{59} + 768 q^{64} - 352 q^{66} + 464 q^{69} - 32 q^{71} + 24 q^{76} - 480 q^{79} - 1068 q^{81} - 600 q^{86} - 300 q^{89} + 1240 q^{91} - 352 q^{94} + O(q^{100}) \)

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

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