↑

Properties

Label 48.26.k
Level $48$
Weight $26$
Character orbit 48.k
Rep. character $\chi_{48}(11,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $396$
Sturm bound $208$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) \(=\) \( 26 \)
Character orbit: \([\chi]\) \(=\) 48.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 48 \)
Character field: \(\Q(i)\)
Sturm bound: \(208\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{26}(48, [\chi])\).

Total New Old
Modular forms 404 404 0
Cusp forms 396 396 0
Eisenstein series 8 8 0

Trace form

\( 396 q - 2 q^{3} - 4 q^{4} - 5523305588 q^{6} - 8 q^{7} + O(q^{10}) \) \( 396 q - 2 q^{3} - 4 q^{4} - 5523305588 q^{6} - 8 q^{7} - 4540039062504 q^{10} - 20197374448688 q^{12} - 4 q^{13} - 4381849800137648 q^{16} - 14303368022877356 q^{18} - 15871852204248204 q^{19} - 1694577218888 q^{21} - 230238065667498824 q^{22} - 227938199064761592 q^{24} - 1754895677587116470 q^{27} + 3047288363637991192 q^{28} - 6496287880423165772 q^{30} - 4 q^{33} + 20105360646896030728 q^{34} + 27706939701358228580 q^{36} - 4 q^{37} + 38776940160342209300 q^{39} + 294658984926999043640 q^{40} + 1081530157623381810936 q^{42} + 70759260127324419852 q^{43} - 596046447753906252 q^{45} - 1222007323158110211112 q^{46} - 1801876743448781389008 q^{48} + 71268218073570706157164 q^{49} + 4433134224914247511704 q^{51} + 5756134814085298649024 q^{52} - 12932966378240319557464 q^{54} - 3044528139046059463656 q^{55} + 5350471673727119884472 q^{58} + 7305481669282406458592 q^{60} - 42722659593243585119604 q^{61} + 61165979604851545460792 q^{64} - 239082820069469799016028 q^{66} + 268332606190952449559068 q^{67} + 1694577218884 q^{69} - 29518977804062085811400 q^{70} - 251825696835894099989240 q^{72} - 817997936512875205550434 q^{75} + 283338617776108384939208 q^{76} - 1365719621441041147925220 q^{78} - 4 q^{81} - 5934022768900071439529536 q^{82} + 10474654185240846656068624 q^{84} - 519338512509131835937504 q^{85} - 986924505491294585698620 q^{87} - 6373625490321367966327264 q^{88} - 28499413854044875120971280 q^{90} - 4264820962706331999054776 q^{91} - 8639820107758019492632292 q^{93} + 8605824511343452771234416 q^{94} + 25100610847768498663477384 q^{96} - 8 q^{97} - 11290219764246812785189300 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{26}^{\mathrm{new}}(48, [\chi])\) into newform subspaces

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