↑

Properties

Label 180.7.c
Level $180$
Weight $7$
Character orbit 180.c
Rep. character $\chi_{180}(91,\cdot)$
Character field $\Q$
Dimension $60$
Newform subspaces $3$
Sturm bound $252$
Trace bound $2$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 180.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(252\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(180, [\chi])\).

Total New Old
Modular forms 224 60 164
Cusp forms 208 60 148
Eisenstein series 16 0 16

Trace form

\( 60 q - 10 q^{2} + 24 q^{4} - 100 q^{8} + O(q^{10}) \) \( 60 q - 10 q^{2} + 24 q^{4} - 100 q^{8} - 750 q^{10} + 5040 q^{13} - 3652 q^{14} - 1404 q^{16} - 6840 q^{17} - 3500 q^{20} + 1680 q^{22} + 187500 q^{25} - 57168 q^{26} - 43080 q^{28} - 57832 q^{29} + 71500 q^{32} + 122364 q^{34} - 48240 q^{37} - 290600 q^{38} + 28500 q^{40} + 87424 q^{41} + 617828 q^{44} + 370440 q^{46} - 1351932 q^{49} - 31250 q^{50} - 655200 q^{52} + 322160 q^{53} + 1164220 q^{56} + 40980 q^{58} + 306336 q^{61} - 1941400 q^{62} - 256164 q^{64} - 133000 q^{65} + 1105600 q^{68} + 639000 q^{70} + 1127160 q^{73} - 992760 q^{74} - 1953816 q^{76} - 1459440 q^{77} + 212000 q^{80} + 302460 q^{82} - 372000 q^{85} - 1719016 q^{86} + 972960 q^{88} + 1287832 q^{89} - 1055160 q^{92} + 1389600 q^{94} - 3975480 q^{97} + 1659390 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(180, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
180.7.c.a 180.c 4.b $12$ $41.410$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(10\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1-\beta _{1})q^{2}+(13-\beta _{1}-\beta _{4})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
180.7.c.b 180.c 4.b $24$ $41.410$ None \(-20\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
180.7.c.c 180.c 4.b $24$ $41.410$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{7}^{\mathrm{old}}(180, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(180, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(4, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 2}\)