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Properties

Label 12.11.d
Level $12$
Weight $11$
Character orbit 12.d
Rep. character $\chi_{12}(7,\cdot)$
Character field $\Q$
Dimension $10$
Newform subspaces $1$
Sturm bound $22$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 12 = 2^{2} \cdot 3 \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 12.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(22\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(12, [\chi])\).

Total New Old
Modular forms 22 10 12
Cusp forms 18 10 8
Eisenstein series 4 0 4

Trace form

\( 10 q + 22 q^{2} - 644 q^{4} + 3116 q^{5} + 2430 q^{6} + 20176 q^{8} - 196830 q^{9} + O(q^{10}) \) \( 10 q + 22 q^{2} - 644 q^{4} + 3116 q^{5} + 2430 q^{6} + 20176 q^{8} - 196830 q^{9} - 369196 q^{10} + 310068 q^{12} - 285100 q^{13} - 2495544 q^{14} + 3590128 q^{16} + 2264420 q^{17} - 433026 q^{18} + 1194248 q^{20} + 3555576 q^{21} - 2139528 q^{22} - 6858432 q^{24} + 23043438 q^{25} + 29599340 q^{26} - 41542224 q^{28} - 46672708 q^{29} + 19963908 q^{30} - 83717408 q^{32} + 22665096 q^{33} + 37514588 q^{34} + 12675852 q^{36} - 194467900 q^{37} - 218769048 q^{38} + 340155488 q^{40} + 276227780 q^{41} - 15919416 q^{42} + 532887504 q^{44} - 61332228 q^{45} - 70057824 q^{46} + 27126576 q^{48} + 653625226 q^{49} + 20815602 q^{50} - 959132296 q^{52} - 1522721956 q^{53} - 47829690 q^{54} - 632703744 q^{56} + 844537752 q^{57} + 1851304388 q^{58} - 1708229736 q^{60} - 3488124604 q^{61} - 806085192 q^{62} - 877634432 q^{64} + 6725245912 q^{65} + 1244885112 q^{66} + 3081993176 q^{68} - 1698239520 q^{69} + 598086768 q^{70} - 397124208 q^{72} + 3090518708 q^{73} - 9824720260 q^{74} + 2750616432 q^{76} - 4577505312 q^{77} + 4510566972 q^{78} + 16715013152 q^{80} + 3874204890 q^{81} + 830592764 q^{82} - 10263359664 q^{84} - 3285444680 q^{85} - 15186172488 q^{86} - 12375555840 q^{88} - 13670065996 q^{89} + 7266884868 q^{90} + 12601016256 q^{92} + 3947087880 q^{93} + 38474881584 q^{94} - 27853204320 q^{96} - 18805077484 q^{97} - 31671844202 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{11}^{\mathrm{new}}(12, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
12.11.d.a 12.d 4.b $10$ $7.624$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(22\) \(0\) \(3116\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(2-\beta _{2})q^{2}+\beta _{1}q^{3}+(-65-2\beta _{1}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{11}^{\mathrm{old}}(12, [\chi])\) into lower level spaces

\( S_{11}^{\mathrm{old}}(12, [\chi]) \cong \) \(S_{11}^{\mathrm{new}}(4, [\chi])\)\(^{\oplus 2}\)