Properties

Label 273.12.bh
Level $273$
Weight $12$
Character orbit 273.bh
Rep. character $\chi_{273}(131,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $704$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 273.bh (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(448\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(273, [\chi])\).

Total New Old
Modular forms 828 704 124
Cusp forms 812 704 108
Eisenstein series 16 0 16

Trace form

\( 704 q + 360448 q^{4} - 31508 q^{7} - 54556 q^{9} + O(q^{10}) \) \( 704 q + 360448 q^{4} - 31508 q^{7} - 54556 q^{9} + 490368 q^{10} - 169590 q^{12} - 1343508 q^{15} - 372328688 q^{16} + 18641930 q^{18} + 91027918 q^{21} + 235355552 q^{22} + 27131904 q^{24} - 3493584780 q^{25} + 376381280 q^{28} - 64316956 q^{30} - 746371812 q^{31} - 1112852724 q^{36} + 473340288 q^{37} + 1506410496 q^{40} - 3377049900 q^{42} + 3150649184 q^{43} - 3077902770 q^{45} - 5754331440 q^{46} + 2923162764 q^{49} - 235870024 q^{51} + 4378707054 q^{54} + 27760900360 q^{57} + 10522189728 q^{58} - 6909538664 q^{60} + 66043856808 q^{61} - 850177286 q^{63} - 729249125424 q^{64} + 24225716478 q^{66} + 40565512096 q^{67} + 208053780040 q^{70} + 15705726986 q^{72} - 20850761136 q^{73} - 57856590096 q^{75} - 80785930940 q^{78} + 152813366224 q^{79} - 82857480332 q^{81} - 219479481864 q^{82} - 376066307154 q^{84} + 134373215744 q^{85} + 194450146332 q^{87} + 192892401064 q^{88} + 26070709288 q^{91} + 68946104254 q^{93} - 602297341992 q^{94} + 883771003470 q^{96} + 235349430028 q^{99} + O(q^{100}) \)

Decomposition of \(S_{12}^{\mathrm{new}}(273, [\chi])\) into newform subspaces

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

Decomposition of \(S_{12}^{\mathrm{old}}(273, [\chi])\) into lower level spaces

\( S_{12}^{\mathrm{old}}(273, [\chi]) \cong \) \(S_{12}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)