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Properties

Label 1110.4.be
Level $1110$
Weight $4$
Character orbit 1110.be
Rep. character $\chi_{1110}(251,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $608$
Sturm bound $912$

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Defining parameters

Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1110.be (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 111 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(912\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1110, [\chi])\).

Total New Old
Modular forms 2768 608 2160
Cusp forms 2704 608 2096
Eisenstein series 64 0 64

Trace form

\( 608 q + O(q^{10}) \) \( 608 q + 296 q^{13} + 4864 q^{16} - 632 q^{19} + 1440 q^{21} - 480 q^{28} - 40 q^{31} - 336 q^{34} + 1792 q^{37} - 8 q^{39} - 624 q^{42} - 200 q^{43} + 640 q^{45} - 12584 q^{49} - 1712 q^{51} - 1184 q^{52} - 720 q^{54} + 120 q^{55} + 3504 q^{57} - 4696 q^{61} + 8640 q^{63} - 2592 q^{66} - 7448 q^{69} + 2528 q^{76} + 1344 q^{78} - 2768 q^{79} - 272 q^{81} + 3936 q^{82} + 9336 q^{87} - 1752 q^{91} - 11744 q^{93} - 8064 q^{94} + 7784 q^{97} + 13680 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1110, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1110, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1110, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(111, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(222, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(555, [\chi])\)\(^{\oplus 2}\)