Properties

Label 12.7.d
Level $12$
Weight $7$
Character orbit 12.d
Rep. character $\chi_{12}(7,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $1$
Sturm bound $14$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 12 = 2^{2} \cdot 3 \)
Weight: \( k \) \(=\) \( 7 \)
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: \(14\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(12, [\chi])\).

Total New Old
Modular forms 14 6 8
Cusp forms 10 6 4
Eisenstein series 4 0 4

Trace form

\( 6q - 10q^{2} + 156q^{4} - 44q^{5} - 162q^{6} + 1136q^{8} - 1458q^{9} + O(q^{10}) \) \( 6q - 10q^{2} + 156q^{4} - 44q^{5} - 162q^{6} + 1136q^{8} - 1458q^{9} + 84q^{10} - 972q^{12} - 3348q^{13} + 4776q^{14} - 9744q^{16} + 12220q^{17} + 2430q^{18} + 17608q^{20} - 9720q^{21} - 13512q^{22} - 7776q^{24} + 56418q^{25} - 59252q^{26} - 17808q^{28} - 84860q^{29} + 57348q^{30} + 61280q^{32} + 4536q^{33} + 109404q^{34} - 37908q^{36} + 20796q^{37} - 128088q^{38} - 195552q^{40} - 65252q^{41} + 210600q^{42} + 445008q^{44} + 10692q^{45} + 81120q^{46} - 276048q^{48} - 111546q^{49} - 743118q^{50} - 179592q^{52} + 470308q^{53} + 39366q^{54} + 793728q^{56} - 204120q^{57} + 529860q^{58} - 723816q^{60} + 12924q^{61} - 513384q^{62} - 642432q^{64} + 321512q^{65} + 771768q^{66} + 690328q^{68} + 541728q^{69} + 938928q^{70} - 276048q^{72} - 1283412q^{73} - 1522916q^{74} + 67824q^{76} - 1487328q^{77} + 396252q^{78} + 1272352q^{80} + 354294q^{81} + 240444q^{82} - 143856q^{84} + 814920q^{85} - 1154568q^{86} + 489600q^{88} + 730924q^{89} - 20412q^{90} - 1338816q^{92} - 83592q^{93} - 390288q^{94} + 624672q^{96} + 3249420q^{97} + 1604918q^{98} + O(q^{100}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(12, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
12.7.d.a \(6\) \(2.761\) 6.0.50898483.1 None \(-10\) \(0\) \(-44\) \(0\) \(q+(-2-\beta _{1})q^{2}-\beta _{2}q^{3}+(3^{3}+2\beta _{1}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{7}^{\mathrm{old}}(12, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(12, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(4, [\chi])\)\(^{\oplus 2}\)