Space of modular forms of level 1694, weight 2, and Character 1694.m

• Label: 1694.2.m
• Level: $1694$
• Weight: $2$
• Character orbit: 1694.m
• Rep. character: $\chi_{1694}(155,\cdot)$
• Character field: $\Q(\zeta_{11})$
• Dimension: $660$
• Sturm bound: $528$

Defining parameters

Level:	\( N \)	\(=\)	\( 1694 = 2 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1694.m (of order \(11\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 121 \)
Character field:			\(\Q(\zeta_{11})\)
Sturm bound:			\(528\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1694, [\chi])\).

	Total	New	Old
Modular forms	2680	660	2020
Cusp forms	2600	660	1940
Eisenstein series	80	0	80

Trace form

660 * q + 2 * q^2 + 4 * q^3 - 66 * q^4 + 4 * q^6 + 2 * q^8 + 672 * q^9 + 10 * q^11 - 18 * q^12 - 108 * q^13 - 20 * q^15 - 66 * q^16 + 12 * q^17 + 10 * q^18 + 28 * q^19 + 12 * q^21 - 34 * q^22 + 8 * q^23 + 4 * q^24 - 42 * q^25 + 40 * q^27 + 44 * q^29 + 40 * q^30 - 48 * q^31 + 2 * q^32 + 44 * q^33 + 28 * q^34 + 4 * q^35 - 54 * q^36 + 24 * q^37 - 104 * q^38 + 56 * q^39 + 12 * q^41 + 48 * q^43 + 10 * q^44 + 24 * q^45 + 32 * q^46 + 48 * q^47 + 4 * q^48 - 66 * q^49 + 30 * q^50 - 126 * q^51 + 24 * q^52 + 32 * q^53 + 64 * q^54 - 28 * q^55 + 58 * q^57 - 72 * q^58 + 60 * q^59 + 24 * q^60 + 64 * q^61 + 16 * q^62 - 66 * q^64 - 44 * q^65 + 26 * q^66 - 48 * q^67 + 12 * q^68 + 72 * q^69 - 36 * q^70 - 48 * q^71 + 10 * q^72 - 20 * q^73 + 52 * q^74 + 100 * q^75 - 38 * q^76 + 8 * q^77 + 64 * q^78 + 4 * q^79 + 740 * q^81 - 44 * q^82 + 100 * q^83 + 12 * q^84 - 108 * q^85 + 44 * q^86 + 72 * q^87 - 56 * q^88 + 60 * q^89 - 104 * q^90 - 108 * q^91 + 8 * q^92 + 120 * q^93 - 144 * q^94 - 88 * q^95 + 4 * q^96 + 84 * q^97 + 2 * q^98 + 130 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(1694, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1694, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1694, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(121, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(242, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(847, [\chi])\)\(^{\oplus 2}\)