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Properties

Label 1476.2.bk
Level $1476$
Weight $2$
Character orbit 1476.bk
Rep. character $\chi_{1476}(133,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $336$
Sturm bound $504$

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Defining parameters

Level: \( N \) \(=\) \( 1476 = 2^{2} \cdot 3^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1476.bk (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 369 \)
Character field: \(\Q(\zeta_{15})\)
Sturm bound: \(504\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1476, [\chi])\).

Total New Old
Modular forms 2064 336 1728
Cusp forms 1968 336 1632
Eisenstein series 96 0 96

Trace form

\( 336 q + 2 q^{3} + 4 q^{5} + 6 q^{9} + O(q^{10}) \) \( 336 q + 2 q^{3} + 4 q^{5} + 6 q^{9} + 3 q^{11} - 6 q^{15} - 8 q^{17} - 18 q^{19} - 16 q^{21} - 9 q^{23} + 42 q^{25} - 4 q^{27} + 12 q^{29} - 16 q^{33} + 4 q^{35} + 26 q^{39} + 5 q^{41} + 9 q^{43} - 4 q^{45} + 18 q^{47} + 30 q^{49} - 16 q^{51} - 76 q^{53} + 28 q^{57} + 22 q^{59} + 18 q^{61} - 8 q^{63} + 14 q^{65} + 9 q^{67} + 12 q^{69} + 82 q^{71} + 12 q^{73} + 2 q^{75} - q^{77} + 62 q^{81} - 78 q^{83} - 96 q^{85} - 6 q^{87} - 40 q^{89} - 32 q^{93} + 2 q^{95} - 42 q^{97} - 26 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1476, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1476, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1476, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(369, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(738, [\chi])\)\(^{\oplus 2}\)