Space of modular forms of level 900, weight 4, and Character 900.i

• Label: 900.4.i
• Level: $900$
• Weight: $4$
• Character orbit: 900.i
• Rep. character: $\chi_{900}(301,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $114$
• Sturm bound: $720$

Defining parameters

Level:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	900.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Sturm bound:			\(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(900, [\chi])\).

	Total	New	Old
Modular forms	1116	114	1002
Cusp forms	1044	114	930
Eisenstein series	72	0	72

Trace form

114 * q + q^3 - 6 * q^7 - 29 * q^9 - q^11 + 12 * q^13 - 126 * q^17 + 30 * q^19 - 80 * q^21 - 126 * q^23 - 56 * q^27 - 336 * q^29 + 12 * q^31 - 135 * q^33 - 240 * q^37 + 516 * q^39 - 427 * q^41 + 129 * q^43 - 246 * q^47 - 2475 * q^49 - 1763 * q^51 - 1224 * q^53 + 467 * q^57 - 413 * q^59 - 438 * q^61 + 80 * q^63 + 399 * q^67 - 1142 * q^69 - 1800 * q^71 + 750 * q^73 - 1032 * q^77 - 132 * q^79 + 919 * q^81 + 384 * q^83 - 1314 * q^87 + 524 * q^89 + 744 * q^91 + 3374 * q^93 + 453 * q^97 - 856 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(900, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(900, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(900, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 2}\)