↑

Properties

Label 3332.2.bo
Level $3332$
Weight $2$
Character orbit 3332.bo
Rep. character $\chi_{3332}(137,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $888$
Sturm bound $1008$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3332 = 2^{2} \cdot 7^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3332.bo (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{21})\)
Sturm bound: \(1008\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3332, [\chi])\).

Total New Old
Modular forms 6120 888 5232
Cusp forms 5976 888 5088
Eisenstein series 144 0 144

Trace form

\( 888 q - 2 q^{3} - 4 q^{5} - 10 q^{7} + 104 q^{9} + O(q^{10}) \) \( 888 q - 2 q^{3} - 4 q^{5} - 10 q^{7} + 104 q^{9} + 4 q^{11} + 20 q^{15} - 4 q^{17} + 6 q^{19} + 8 q^{21} + 74 q^{25} + 16 q^{27} + 20 q^{29} + 18 q^{31} - 2 q^{33} + 18 q^{35} + 16 q^{37} + 38 q^{39} + 28 q^{41} - 36 q^{43} + 70 q^{45} - 4 q^{47} - 8 q^{49} - 50 q^{53} + 66 q^{55} - 32 q^{57} + 18 q^{59} - 2 q^{61} + 48 q^{63} + 10 q^{65} - 12 q^{69} - 20 q^{71} - 46 q^{73} - 40 q^{75} - 12 q^{77} + 32 q^{79} + 42 q^{81} - 80 q^{83} - 154 q^{87} - 190 q^{89} + 24 q^{91} + 6 q^{93} - 16 q^{95} + 68 q^{97} - 20 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3332, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3332, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3332, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(833, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1666, [\chi])\)\(^{\oplus 2}\)