Space of modular forms of level 1014, weight 2, and Character 1014.m

• Label: 1014.2.m
• Level: $1014$
• Weight: $2$
• Character orbit: 1014.m
• Rep. character: $\chi_{1014}(79,\cdot)$
• Character field: $\Q(\zeta_{13})$
• Dimension: $336$
• Sturm bound: $364$

Defining parameters

Level:	\( N \)	\(=\)	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1014.m (of order \(13\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 169 \)
Character field:			\(\Q(\zeta_{13})\)
Sturm bound:			\(364\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1014, [\chi])\).

	Total	New	Old
Modular forms	2232	336	1896
Cusp forms	2136	336	1800
Eisenstein series	96	0	96

Trace form

336 * q + 2 * q^2 + 2 * q^3 - 28 * q^4 + 4 * q^5 + 4 * q^7 + 2 * q^8 - 28 * q^9 + 8 * q^10 + 16 * q^11 + 2 * q^12 - 14 * q^13 + 8 * q^14 + 8 * q^15 - 28 * q^16 + 12 * q^17 + 2 * q^18 + 28 * q^19 + 4 * q^20 + 12 * q^21 - 48 * q^22 + 16 * q^23 - 4 * q^25 + 14 * q^26 + 2 * q^27 + 4 * q^28 + 12 * q^29 + 4 * q^30 - 16 * q^31 + 2 * q^32 + 8 * q^33 + 20 * q^34 + 32 * q^35 - 28 * q^36 + 40 * q^37 + 8 * q^38 + 14 * q^39 - 18 * q^40 + 52 * q^41 + 4 * q^42 + 32 * q^43 + 16 * q^44 + 4 * q^45 + 24 * q^46 + 40 * q^47 + 2 * q^48 - 44 * q^49 + 30 * q^50 + 12 * q^51 + 12 * q^52 - 78 * q^53 - 32 * q^55 + 8 * q^56 + 12 * q^57 - 16 * q^58 + 56 * q^59 - 44 * q^60 + 52 * q^61 + 24 * q^62 + 4 * q^63 - 28 * q^64 + 76 * q^65 + 16 * q^66 - 72 * q^67 + 12 * q^68 + 16 * q^69 - 152 * q^70 - 76 * q^71 + 2 * q^72 + 72 * q^73 - 146 * q^74 + 30 * q^75 - 24 * q^76 + 104 * q^77 + 12 * q^78 + 52 * q^79 + 4 * q^80 - 28 * q^81 + 28 * q^82 + 72 * q^83 + 12 * q^84 - 26 * q^85 - 108 * q^86 - 20 * q^87 + 4 * q^88 + 76 * q^89 + 8 * q^90 - 4 * q^91 + 16 * q^92 - 154 * q^93 - 4 * q^94 - 88 * q^95 - 68 * q^97 + 66 * q^98 + 16 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(1014, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1014, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1014, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(338, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(507, [\chi])\)\(^{\oplus 2}\)