Properties

Label 12.7.c
Level $12$
Weight $7$
Character orbit 12.c
Rep. character $\chi_{12}(5,\cdot)$
Character field $\Q$
Dimension $2$
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.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
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 15 2 13
Cusp forms 9 2 7
Eisenstein series 6 0 6

Trace form

\( 2 q - 6 q^{3} + 484 q^{7} - 1422 q^{9} + O(q^{10}) \) \( 2 q - 6 q^{3} + 484 q^{7} - 1422 q^{9} + 5236 q^{13} - 8640 q^{15} + 11572 q^{19} - 1452 q^{21} - 20590 q^{25} + 12906 q^{27} - 40892 q^{31} + 95040 q^{33} - 93548 q^{37} - 15708 q^{39} + 137236 q^{43} + 51840 q^{45} - 118170 q^{49} - 380160 q^{51} + 570240 q^{55} - 34716 q^{57} + 49588 q^{61} - 344124 q^{63} - 168716 q^{67} + 501120 q^{69} - 227612 q^{73} + 61770 q^{75} - 319484 q^{79} + 959202 q^{81} - 2280960 q^{85} + 665280 q^{87} + 1267112 q^{91} + 122676 q^{93} + 1799044 q^{97} - 570240 q^{99} + O(q^{100}) \)

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.c.a \(2\) \(2.761\) \(\Q(\sqrt{-5}) \) None \(0\) \(-6\) \(0\) \(484\) \(q+(-3+\beta )q^{3}+6\beta q^{5}+242q^{7}+(-711+\cdots)q^{9}+\cdots\)

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

\( S_{7}^{\mathrm{old}}(12, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 2}\)