↑

Properties

Label 3150.3.bc
Level $3150$
Weight $3$
Character orbit 3150.bc
Rep. character $\chi_{3150}(1501,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $608$
Sturm bound $2160$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 3150.bc (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(2160\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(3150, [\chi])\).

Total New Old
Modular forms 2928 608 2320
Cusp forms 2832 608 2224
Eisenstein series 96 0 96

Trace form

\( 608 q + 1216 q^{4} - 2 q^{7} - 12 q^{9} + O(q^{10}) \) \( 608 q + 1216 q^{4} - 2 q^{7} - 12 q^{9} + 12 q^{11} + 30 q^{13} + 12 q^{14} + 2432 q^{16} - 54 q^{17} + 32 q^{18} - 32 q^{21} + 6 q^{23} - 72 q^{26} - 54 q^{27} - 4 q^{28} + 84 q^{29} - 24 q^{36} - 22 q^{37} + 78 q^{39} - 252 q^{41} - 40 q^{42} - 16 q^{43} + 24 q^{44} - 12 q^{46} + 2 q^{49} - 46 q^{51} + 60 q^{52} + 108 q^{53} - 144 q^{54} + 24 q^{56} + 138 q^{57} + 24 q^{58} + 254 q^{63} + 4864 q^{64} + 96 q^{66} - 140 q^{67} - 108 q^{68} - 210 q^{69} + 468 q^{71} + 64 q^{72} - 72 q^{74} + 282 q^{77} - 160 q^{78} + 76 q^{79} + 76 q^{81} - 756 q^{83} - 64 q^{84} + 24 q^{86} + 264 q^{87} - 414 q^{89} - 186 q^{91} + 12 q^{92} - 62 q^{93} - 114 q^{97} - 384 q^{98} + 298 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(3150, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(3150, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(3150, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(630, [\chi])\)\(^{\oplus 2}\)