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Properties

Label 1530.2.bc
Level $1530$
Weight $2$
Character orbit 1530.bc
Rep. character $\chi_{1530}(451,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $120$
Sturm bound $648$

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Defining parameters

Level: \( N \) \(=\) \( 1530 = 2 \cdot 3^{2} \cdot 5 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1530.bc (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 17 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(648\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1530, [\chi])\).

Total New Old
Modular forms 1360 120 1240
Cusp forms 1232 120 1112
Eisenstein series 128 0 128

Trace form

\( 120 q + O(q^{10}) \) \( 120 q - 8 q^{11} - 16 q^{14} - 120 q^{16} - 16 q^{19} - 16 q^{22} - 64 q^{23} + 16 q^{29} - 16 q^{31} - 16 q^{34} - 16 q^{35} + 48 q^{37} + 64 q^{41} - 24 q^{43} + 32 q^{44} + 32 q^{46} + 48 q^{49} + 8 q^{50} + 16 q^{52} + 80 q^{53} + 24 q^{59} + 16 q^{61} - 48 q^{62} + 16 q^{65} + 16 q^{67} - 96 q^{71} + 16 q^{76} - 64 q^{77} - 32 q^{79} + 24 q^{82} + 56 q^{83} - 16 q^{86} + 24 q^{88} - 48 q^{91} + 16 q^{92} - 32 q^{94} - 32 q^{95} + 56 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1530, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1530, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1530, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(51, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(85, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(102, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(153, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(170, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(255, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(306, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(510, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(765, [\chi])\)\(^{\oplus 2}\)