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Properties

Label 3150.2.l
Level $3150$
Weight $2$
Character orbit 3150.l
Rep. character $\chi_{3150}(1201,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $304$
Sturm bound $1440$

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Defining parameters

Level: \( N \) \(=\) \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3150.l (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(1440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3150, [\chi])\).

Total New Old
Modular forms 1488 304 1184
Cusp forms 1392 304 1088
Eisenstein series 96 0 96

Trace form

\( 304 q - 152 q^{4} + 4 q^{6} - 2 q^{7} + 2 q^{9} + O(q^{10}) \) \( 304 q - 152 q^{4} + 4 q^{6} - 2 q^{7} + 2 q^{9} + 8 q^{11} + 2 q^{13} - 2 q^{14} - 152 q^{16} - 2 q^{17} - 4 q^{18} - 4 q^{19} - 6 q^{21} + 20 q^{23} - 2 q^{24} + 8 q^{26} + 12 q^{27} - 2 q^{28} + 10 q^{29} + 2 q^{31} - 18 q^{33} + 8 q^{36} + 2 q^{37} + 24 q^{38} - 22 q^{39} + 30 q^{41} + 22 q^{42} + 2 q^{43} - 4 q^{44} + 6 q^{46} - 6 q^{47} + 10 q^{49} - 12 q^{51} - 4 q^{52} - 16 q^{53} + 10 q^{54} + 4 q^{56} + 34 q^{57} + 12 q^{58} + 2 q^{59} + 20 q^{61} + 20 q^{62} - 42 q^{63} + 304 q^{64} - 8 q^{66} + 14 q^{67} + 4 q^{68} + 26 q^{69} + 44 q^{71} + 8 q^{72} - 28 q^{73} + 12 q^{74} - 4 q^{76} + 14 q^{77} + 16 q^{78} - 16 q^{79} + 50 q^{81} - 40 q^{83} - 6 q^{84} - 8 q^{86} + 32 q^{87} + 36 q^{89} - 16 q^{91} - 10 q^{92} - 70 q^{93} - 12 q^{94} - 2 q^{96} + 2 q^{97} + 24 q^{98} + 26 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3150, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3150, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3150, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(630, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1575, [\chi])\)\(^{\oplus 2}\)