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Properties

Label 1870.2.p
Level $1870$
Weight $2$
Character orbit 1870.p
Rep. character $\chi_{1870}(307,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $192$
Sturm bound $648$

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Defining parameters

Level: \( N \) \(=\) \( 1870 = 2 \cdot 5 \cdot 11 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1870.p (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
Character field: \(\Q(i)\)
Sturm bound: \(648\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1870, [\chi])\).

Total New Old
Modular forms 664 192 472
Cusp forms 632 192 440
Eisenstein series 32 0 32

Trace form

\( 192 q - 8 q^{3} + O(q^{10}) \) \( 192 q - 8 q^{3} + 8 q^{11} + 8 q^{12} + 8 q^{15} - 192 q^{16} - 8 q^{20} + 8 q^{22} + 8 q^{23} + 24 q^{25} + 16 q^{26} + 16 q^{27} - 192 q^{36} + 72 q^{37} + 48 q^{38} - 80 q^{42} - 88 q^{45} - 24 q^{47} + 8 q^{48} - 120 q^{53} + 56 q^{55} - 16 q^{56} - 64 q^{58} - 24 q^{60} + 32 q^{66} - 8 q^{67} + 32 q^{70} - 80 q^{71} + 136 q^{75} + 16 q^{77} + 32 q^{78} - 208 q^{81} + 32 q^{82} + 16 q^{86} + 8 q^{88} - 96 q^{91} - 8 q^{92} + 80 q^{93} - 40 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1870, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1870, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1870, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 2}\)