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Properties

Label 3021.2.bm
Level $3021$
Weight $2$
Character orbit 3021.bm
Rep. character $\chi_{3021}(115,\cdot)$
Character field $\Q(\zeta_{26})$
Dimension $1968$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 3021 = 3 \cdot 19 \cdot 53 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3021.bm (of order \(26\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 53 \)
Character field: \(\Q(\zeta_{26})\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3021, [\chi])\).

Total New Old
Modular forms 4368 1968 2400
Cusp forms 4272 1968 2304
Eisenstein series 96 0 96

Trace form

\( 1968 q + 176 q^{4} + 4 q^{6} + 16 q^{7} + 104 q^{8} + 164 q^{9} + O(q^{10}) \) \( 1968 q + 176 q^{4} + 4 q^{6} + 16 q^{7} + 104 q^{8} + 164 q^{9} - 8 q^{10} - 8 q^{11} + 8 q^{15} - 184 q^{16} + 32 q^{17} - 12 q^{24} + 172 q^{25} - 32 q^{28} + 24 q^{29} + 52 q^{31} + 156 q^{33} - 176 q^{36} - 48 q^{37} + 4 q^{40} - 52 q^{41} + 20 q^{42} + 104 q^{43} - 272 q^{44} - 12 q^{46} - 28 q^{47} - 140 q^{49} - 208 q^{50} + 328 q^{52} + 28 q^{53} + 48 q^{54} + 364 q^{56} + 4 q^{57} - 208 q^{58} - 40 q^{59} - 44 q^{60} - 52 q^{61} + 72 q^{62} - 16 q^{63} + 56 q^{64} - 8 q^{66} - 52 q^{67} + 144 q^{68} + 16 q^{69} + 408 q^{70} + 52 q^{73} + 52 q^{74} + 208 q^{75} - 48 q^{77} - 16 q^{78} + 104 q^{79} - 164 q^{81} + 116 q^{82} - 52 q^{87} - 52 q^{88} + 236 q^{89} + 8 q^{90} - 136 q^{91} - 468 q^{92} - 36 q^{93} + 8 q^{96} + 92 q^{97} + 52 q^{98} + 8 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3021, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3021, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3021, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(53, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(159, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1007, [\chi])\)\(^{\oplus 2}\)