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Properties

Label 2960.2.hx
Level $2960$
Weight $2$
Character orbit 2960.hx
Rep. character $\chi_{2960}(17,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $1344$
Sturm bound $912$

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Defining parameters

Level: \( N \) \(=\) \( 2960 = 2^{4} \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2960.hx (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 185 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(912\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2960, [\chi])\).

Total New Old
Modular forms 5616 1392 4224
Cusp forms 5328 1344 3984
Eisenstein series 288 48 240

Trace form

\( 1344 q + 12 q^{3} - 12 q^{5} + 12 q^{7} + O(q^{10}) \) \( 1344 q + 12 q^{3} - 12 q^{5} + 12 q^{7} + 36 q^{11} - 12 q^{13} + 12 q^{15} - 18 q^{17} - 24 q^{21} + 6 q^{23} - 18 q^{25} - 18 q^{27} + 24 q^{31} - 30 q^{33} + 12 q^{35} - 12 q^{37} - 24 q^{41} + 24 q^{43} - 12 q^{45} + 6 q^{47} + 24 q^{51} - 12 q^{53} + 42 q^{55} - 12 q^{57} - 24 q^{61} + 6 q^{63} - 12 q^{65} + 12 q^{67} + 36 q^{69} + 24 q^{71} + 60 q^{73} + 24 q^{75} - 54 q^{77} - 144 q^{79} - 24 q^{81} + 12 q^{83} - 18 q^{85} - 54 q^{87} + 24 q^{89} - 120 q^{91} - 24 q^{93} + 12 q^{95} - 18 q^{97} - 192 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2960, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2960, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2960, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(185, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(370, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(740, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1480, [\chi])\)\(^{\oplus 2}\)