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

• Label: 1452.3.k
• Level: $1452$
• Weight: $3$
• Character orbit: 1452.k
• Rep. character: $\chi_{1452}(487,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $864$
• Sturm bound: $792$

Defining parameters

Level:	\( N \)	\(=\)	\( 1452 = 2^{2} \cdot 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1452.k (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 44 \)
Character field:			\(\Q(\zeta_{10})\)
Sturm bound:			\(792\)

Dimensions

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

	Total	New	Old
Modular forms	2208	864	1344
Cusp forms	2016	864	1152
Eisenstein series	192	0	192

Trace form

864 * q - 4 * q^2 - 12 * q^4 + 20 * q^8 + 648 * q^9 - 8 * q^10 - 24 * q^12 - 58 * q^14 - 104 * q^16 - 18 * q^18 + 50 * q^20 + 54 * q^24 - 1064 * q^25 + 262 * q^26 + 102 * q^28 - 64 * q^29 + 108 * q^30 + 56 * q^32 + 720 * q^34 + 36 * q^36 - 288 * q^37 + 122 * q^38 + 218 * q^40 - 48 * q^41 - 108 * q^42 - 98 * q^46 - 48 * q^48 + 1736 * q^49 - 214 * q^50 - 478 * q^52 + 448 * q^53 - 1028 * q^56 - 586 * q^58 - 72 * q^60 + 96 * q^61 - 40 * q^62 + 492 * q^64 + 160 * q^65 - 264 * q^68 + 720 * q^70 + 90 * q^72 + 168 * q^73 + 410 * q^74 + 256 * q^76 + 1104 * q^78 + 866 * q^80 - 1944 * q^81 + 450 * q^82 + 324 * q^84 + 336 * q^85 - 788 * q^86 - 352 * q^89 - 36 * q^90 - 1106 * q^92 - 144 * q^93 - 862 * q^94 - 270 * q^96 - 16 * q^97 - 1768 * 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

\( S_{3}^{\mathrm{old}}(1452, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(132, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(484, [\chi])\)\(^{\oplus 2}\)