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Properties

Label 3150.2.q
Level $3150$
Weight $2$
Character orbit 3150.q
Rep. character $\chi_{3150}(631,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $296$
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.q (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 2944 296 2648
Cusp forms 2816 296 2520
Eisenstein series 128 0 128

Trace form

\( 296 q + 2 q^{2} - 74 q^{4} + 18 q^{5} + 2 q^{8} + O(q^{10}) \) \( 296 q + 2 q^{2} - 74 q^{4} + 18 q^{5} + 2 q^{8} + 2 q^{10} - 4 q^{11} - 12 q^{13} - 4 q^{14} - 74 q^{16} + 4 q^{17} + 24 q^{19} - 12 q^{20} + 12 q^{22} - 28 q^{23} - 14 q^{25} + 12 q^{26} - 12 q^{29} + 24 q^{31} - 8 q^{32} - 18 q^{34} + 4 q^{35} + 10 q^{37} - 24 q^{38} + 2 q^{40} + 12 q^{41} - 8 q^{43} - 4 q^{44} + 20 q^{46} + 28 q^{47} + 296 q^{49} + 6 q^{50} - 12 q^{52} - 2 q^{53} - 100 q^{55} - 4 q^{56} + 4 q^{58} + 36 q^{59} + 60 q^{61} + 16 q^{62} - 74 q^{64} + 82 q^{65} + 12 q^{67} + 4 q^{68} - 4 q^{70} - 48 q^{71} + 76 q^{73} + 92 q^{74} - 16 q^{76} - 24 q^{77} + 56 q^{79} - 2 q^{80} + 44 q^{82} - 52 q^{83} + 58 q^{85} - 20 q^{86} - 8 q^{88} - 34 q^{89} + 4 q^{91} + 32 q^{92} - 20 q^{95} - 16 q^{97} + 2 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3150, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 4}\)