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Properties

Label 2415.2.cy
Level $2415$
Weight $2$
Character orbit 2415.cy
Rep. character $\chi_{2415}(26,\cdot)$
Character field $\Q(\zeta_{66})$
Dimension $5120$
Sturm bound $768$

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Defining parameters

Level: \( N \) \(=\) \( 2415 = 3 \cdot 5 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2415.cy (of order \(66\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 483 \)
Character field: \(\Q(\zeta_{66})\)
Sturm bound: \(768\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2415, [\chi])\).

Total New Old
Modular forms 7840 5120 2720
Cusp forms 7520 5120 2400
Eisenstein series 320 0 320

Trace form

\( 5120 q - 256 q^{4} + 4 q^{9} + O(q^{10}) \) \( 5120 q - 256 q^{4} + 4 q^{9} + 224 q^{16} - 16 q^{18} + 120 q^{21} + 64 q^{22} - 36 q^{24} + 256 q^{25} - 4 q^{30} - 48 q^{33} - 56 q^{36} - 16 q^{37} - 24 q^{39} + 48 q^{42} + 144 q^{43} + 36 q^{45} + 20 q^{46} + 92 q^{49} + 4 q^{51} - 72 q^{54} - 72 q^{57} - 200 q^{58} + 72 q^{61} - 90 q^{63} + 384 q^{64} + 120 q^{66} - 48 q^{67} + 24 q^{70} - 160 q^{72} - 472 q^{78} + 28 q^{79} - 28 q^{81} - 144 q^{82} + 22 q^{84} + 708 q^{87} - 16 q^{88} + 16 q^{91} - 52 q^{93} + 96 q^{94} + 120 q^{96} - 392 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2415, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2415, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2415, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(483, [\chi])\)\(^{\oplus 2}\)