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Properties

Label 3150.2.bm
Level $3150$
Weight $2$
Character orbit 3150.bm
Rep. character $\chi_{3150}(1301,\cdot)$
Character field $\Q(\zeta_{6})$
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.bm (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
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

\( 304 q + 152 q^{4} + 2 q^{7} - 12 q^{9} + O(q^{10}) \) \( 304 q + 152 q^{4} + 2 q^{7} - 12 q^{9} + 12 q^{11} + 6 q^{14} - 152 q^{16} - 4 q^{18} - 14 q^{21} - 24 q^{23} + 4 q^{28} + 12 q^{29} - 12 q^{36} - 8 q^{37} + 12 q^{39} + 8 q^{42} + 4 q^{43} - 24 q^{46} + 4 q^{49} + 20 q^{51} + 6 q^{56} + 24 q^{57} + 12 q^{58} - 40 q^{63} - 304 q^{64} - 28 q^{67} + 16 q^{72} + 36 q^{74} - 66 q^{77} - 40 q^{78} - 4 q^{79} - 20 q^{81} + 2 q^{84} - 24 q^{86} + 24 q^{91} - 24 q^{92} + 88 q^{93} + 112 q^{99} + O(q^{100}) \)

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

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