Space of modular forms of level 1452, weight 3, and Character 1452.be

• Label: 1452.3.be
• Level: $1452$
• Weight: $3$
• Character orbit: 1452.be
• Rep. character: $\chi_{1452}(31,\cdot)$
• Character field: $\Q(\zeta_{110})$
• Dimension: $10560$
• Sturm bound: $792$

Defining parameters

Level:	\( N \)	\(=\)	\( 1452 = 2^{2} \cdot 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1452.be (of order \(110\) and degree \(40\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 484 \)
Character field:			\(\Q(\zeta_{110})\)
Sturm bound:			\(792\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1452, [\chi])\).

	Total	New	Old
Modular forms	21280	10560	10720
Cusp forms	20960	10560	10400
Eisenstein series	320	0	320

Trace form

10560 * q - 4 * q^2 - 12 * q^4 + 20 * q^8 + 7920 * q^9 - 8 * q^10 - 24 * q^12 - 42 * q^14 - 56 * q^16 - 18 * q^18 - 30 * q^20 + 54 * q^22 + 54 * q^24 + 1336 * q^25 + 150 * q^26 + 102 * q^28 - 64 * q^29 + 108 * q^30 + 56 * q^32 - 24 * q^33 + 144 * q^34 + 36 * q^36 - 288 * q^37 + 122 * q^38 + 218 * q^40 - 48 * q^41 - 108 * q^42 - 316 * q^44 - 98 * q^46 - 48 * q^48 - 1624 * q^49 - 2502 * q^50 - 192 * q^52 + 624 * q^53 + 882 * q^56 - 276 * q^58 + 96 * q^61 - 1250 * q^62 + 372 * q^64 + 160 * q^65 + 24 * q^66 - 264 * q^68 + 312 * q^70 + 90 * q^72 + 168 * q^73 + 410 * q^74 + 1906 * q^76 + 496 * q^77 - 90 * q^78 + 826 * q^80 - 23760 * q^81 + 330 * q^82 + 324 * q^84 + 336 * q^85 - 316 * q^86 + 112 * q^88 - 224 * q^89 - 36 * q^90 - 826 * q^92 - 144 * q^93 - 862 * q^94 - 270 * q^96 + 80 * q^97 - 3000 * q^98

Decomposition of \(S_{3}^{\mathrm{new}}(1452, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(1452, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1452, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(484, [\chi])\)\(^{\oplus 2}\)