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Properties

Label 3150.3.w
Level $3150$
Weight $3$
Character orbit 3150.w
Rep. character $\chi_{3150}(451,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $252$
Sturm bound $2160$

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Defining parameters

Level: \( N \) \(=\) \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 3150.w (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
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 2976 252 2724
Cusp forms 2784 252 2532
Eisenstein series 192 0 192

Trace form

\( 252 q - 252 q^{4} - 8 q^{7} + O(q^{10}) \) \( 252 q - 252 q^{4} - 8 q^{7} + 6 q^{11} - 20 q^{14} - 504 q^{16} - 30 q^{17} + 6 q^{19} + 24 q^{22} + 18 q^{23} - 24 q^{26} - 4 q^{28} + 112 q^{29} - 30 q^{31} - 46 q^{37} - 108 q^{38} + 88 q^{43} + 12 q^{44} + 44 q^{46} - 198 q^{47} + 144 q^{49} - 48 q^{52} - 70 q^{53} - 16 q^{56} - 40 q^{58} + 78 q^{59} - 90 q^{61} + 2016 q^{64} + 34 q^{67} + 60 q^{68} + 216 q^{71} + 30 q^{73} - 112 q^{74} + 102 q^{77} - 126 q^{79} - 120 q^{82} - 128 q^{86} - 24 q^{88} - 330 q^{89} - 752 q^{91} - 72 q^{92} - 156 q^{94} + 24 q^{98} + O(q^{100}) \)

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

\( S_{3}^{\mathrm{old}}(3150, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(630, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1050, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1575, [\chi])\)\(^{\oplus 2}\)