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Properties

Label 3120.2.by
Level $3120$
Weight $2$
Character orbit 3120.by
Rep. character $\chi_{3120}(781,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $384$
Sturm bound $1344$

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Defining parameters

Level: \( N \) \(=\) \( 3120 = 2^{4} \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3120.by (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Sturm bound: \(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3120, [\chi])\).

Total New Old
Modular forms 1360 384 976
Cusp forms 1328 384 944
Eisenstein series 32 0 32

Trace form

\( 384 q - 16 q^{4} + O(q^{10}) \) \( 384 q - 16 q^{4} + 8 q^{10} - 32 q^{11} - 16 q^{14} - 16 q^{15} + 8 q^{16} + 16 q^{18} - 16 q^{19} + 16 q^{22} + 8 q^{24} - 64 q^{29} - 8 q^{34} - 8 q^{36} - 64 q^{37} + 32 q^{43} + 16 q^{44} - 8 q^{46} - 384 q^{49} - 16 q^{50} + 16 q^{51} + 64 q^{53} + 8 q^{54} - 96 q^{56} - 128 q^{58} + 32 q^{61} + 48 q^{62} + 32 q^{63} + 32 q^{64} + 48 q^{66} + 32 q^{67} + 48 q^{68} + 32 q^{69} - 16 q^{72} + 16 q^{74} + 8 q^{76} + 64 q^{77} + 32 q^{79} - 384 q^{81} - 96 q^{84} - 32 q^{85} - 128 q^{86} - 16 q^{88} - 160 q^{92} - 88 q^{94} + 112 q^{98} - 32 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3120, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3120, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3120, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(208, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(624, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1040, [\chi])\)\(^{\oplus 2}\)