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Properties

Label 3150.3.ek
Level $3150$
Weight $3$
Character orbit 3150.ek
Rep. character $\chi_{3150}(37,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $3200$
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.ek (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 175 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(2160\)

Dimensions

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

Total New Old
Modular forms 23296 3200 20096
Cusp forms 22784 3200 19584
Eisenstein series 512 0 512

Trace form

\( 3200 q - 4 q^{5} + 20 q^{7} + O(q^{10}) \) \( 3200 q - 4 q^{5} + 20 q^{7} - 16 q^{10} - 1600 q^{16} + 260 q^{17} + 64 q^{22} + 64 q^{23} + 68 q^{25} + 112 q^{28} + 400 q^{29} + 52 q^{35} - 100 q^{37} - 32 q^{38} + 232 q^{43} - 220 q^{47} - 192 q^{50} - 164 q^{53} - 440 q^{55} - 128 q^{58} + 400 q^{59} - 1200 q^{62} - 116 q^{65} + 16 q^{67} + 400 q^{68} - 464 q^{70} - 4 q^{73} - 4 q^{77} + 16 q^{80} - 512 q^{82} + 2080 q^{83} + 544 q^{85} - 96 q^{88} - 1500 q^{89} - 96 q^{92} + 92 q^{95} - 1024 q^{97} - 352 q^{98} + O(q^{100}) \)

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

\( S_{3}^{\mathrm{old}}(3150, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1050, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1575, [\chi])\)\(^{\oplus 2}\)