Space of modular forms of level 144, weight 14, and Character 144.i

• Label: 144.14.i
• Level: $144$
• Weight: $14$
• Character orbit: 144.i
• Rep. character: $\chi_{144}(49,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $154$
• Sturm bound: $336$

Defining parameters

Level:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	144.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Sturm bound:			\(336\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(144, [\chi])\).

	Total	New	Old
Modular forms	636	158	478
Cusp forms	612	154	458
Eisenstein series	24	4	20

Trace form

154 * q + 2 * q^3 - q^5 + q^7 + 327236 * q^9 + 10629367 * q^11 - q^13 + 55638485 * q^15 + 55174600 * q^17 + 4 * q^19 + 339269949 * q^21 - 888215333 * q^23 - 17822265626 * q^25 - 4041096064 * q^27 + 492157011 * q^29 + 365470567 * q^31 + 1308681667 * q^33 - 46559781246 * q^35 - 4 * q^37 + 66171782321 * q^39 - 10736753403 * q^41 - 29899698185 * q^43 - 4921671877 * q^45 - 144917157615 * q^47 - 982731391272 * q^49 + 188244641914 * q^51 - 4 * q^53 - 2441406246 * q^55 - 400446522082 * q^57 + 1007342779705 * q^59 - q^61 - 34515512607 * q^63 + 159596611217 * q^65 + q^67 - 713844542195 * q^69 + 786562792184 * q^71 - 83657506912 * q^73 - 4053933960914 * q^75 - 117669910155 * q^77 + q^79 + 1700626542428 * q^81 + 1553648128733 * q^83 - 1220703126 * q^85 - 6577453283745 * q^87 - 11697483564852 * q^89 - 11877730693942 * q^91 - 2499477653083 * q^93 - 111801093292 * q^95 + 4656132991373 * q^97 + 5326230176305 * q^99

Decomposition of \(S_{14}^{\mathrm{new}}(144, [\chi])\) into newform subspaces

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

Decomposition of \(S_{14}^{\mathrm{old}}(144, [\chi])\) into lower level spaces

\( S_{14}^{\mathrm{old}}(144, [\chi]) \simeq \) \(S_{14}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 2}\)