Properties

Label 900.3.bi
Level $900$
Weight $3$
Character orbit 900.bi
Rep. character $\chi_{900}(37,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $200$
Sturm bound $540$

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Defining parameters

Level: \( N \) \(=\) \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 900.bi (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(540\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(900, [\chi])\).

Total New Old
Modular forms 2976 200 2776
Cusp forms 2784 200 2584
Eisenstein series 192 0 192

Trace form

\( 200q + 6q^{5} - 2q^{7} + O(q^{10}) \) \( 200q + 6q^{5} - 2q^{7} + 6q^{13} + 32q^{17} - 100q^{19} - 66q^{23} - 80q^{25} - 100q^{29} + 44q^{35} - 6q^{37} + 80q^{41} - 114q^{43} - 158q^{47} - 34q^{53} + 108q^{55} + 250q^{59} - 120q^{61} - 112q^{65} - 90q^{67} + 60q^{71} + 142q^{73} - 100q^{77} + 200q^{79} - 56q^{83} + 368q^{85} + 700q^{89} + 304q^{95} - 50q^{97} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(900, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(900, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(900, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 2}\)