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Properties

Label 1395.2.by
Level $1395$
Weight $2$
Character orbit 1395.by
Rep. character $\chi_{1395}(64,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $312$
Sturm bound $384$

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Defining parameters

Level: \( N \) \(=\) \( 1395 = 3^{2} \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1395.by (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 155 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(384\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1395, [\chi])\).

Total New Old
Modular forms 800 328 472
Cusp forms 736 312 424
Eisenstein series 64 16 48

Trace form

\( 312 q + 74 q^{4} + 10 q^{5} + O(q^{10}) \) \( 312 q + 74 q^{4} + 10 q^{5} - 4 q^{10} + 14 q^{11} + 12 q^{14} - 70 q^{16} - 10 q^{19} - 7 q^{20} - 2 q^{25} - 36 q^{26} + 8 q^{29} + 10 q^{31} - 10 q^{34} - 24 q^{35} - 16 q^{41} + 18 q^{44} - 10 q^{46} + 110 q^{49} - 57 q^{50} - 30 q^{55} + 224 q^{56} - 38 q^{59} + 8 q^{61} + 52 q^{64} + 31 q^{65} - 23 q^{70} - 36 q^{71} - 48 q^{74} + 72 q^{76} - 30 q^{79} + 10 q^{80} + 6 q^{85} + 26 q^{86} - 24 q^{89} - 12 q^{91} - 168 q^{94} - 43 q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1395, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1395, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1395, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(155, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(465, [\chi])\)\(^{\oplus 2}\)